RECERCAT - Articles publicats en revistes (Matemàtica Aplicada i Anàlisi)

Equidistribution of Fekete Points on the Sphere

Equidistribution of Fekete Points on the Sphere Marzo Sánchez, Jordi; Ortega Cerdà, Joaquim Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing Carroll, Tom; Ortega Cerdà, Joaquim By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.

Millora de l'actuació docent del professorat de Matemàtiques

Millora de l'actuació docent del professorat de Matemàtiques Benseny, Antoni; Cascante, Ma. Carme (Maria Carme); Gispert Brasó, Joan; Verdú, B. (Buenaventura) Aquest article és fruit de la recerca duta a terme en el marc del projecte conjunt REDICE08, PID08, PID09 'Com motivar, com adequar l"avaluació continuada i com mesurar el treball a les assignatures de Matemàtiques' durant els cursos 2008 2009 i 2009-2010. El projecte aborda temes relacionats amb els resultats de les enquestes sobre l"actuació docent del professorat a l"ensenyament de Matemàtiques de la Universitat de Barcelona (UB), en què l"alumnat posa de manifest, en general, un baixa motivació del professorat i un elevat volum de feina en les assignatures. Com a resultat de l"estudi i de la pràctica docent en les assignatures involucrades en el projecte citat abans, es desprèn que la motivació de l"alumnat s"aconsegueix sumant esforços en diferents direccions: d"una banda, cal una tria adequada i una bona comunicació dels continguts, que fomenti el diàleg amb l"alumnat; d"altra banda, cal que l"avaluació continuada presenti un esglaonament progressiu en la dificultat de les activitats no presencials i una atenció continuada a l"alumnat mentre les duu a terme. Finalment, cal quantificar la dedicació de l"alumnat a les diferents activitats no presencials, ja que serveix de gran ajuda al professorat a l"hora d"adequar-les a la dedicació requerida, i ponderar les diferents activitats d"avaluació acreditativa en la qualificació de forma proporcional a aquesta dedicació. La motivació pren molta força com a element clau que cal tenir en compte en el bon desenvolupament de la docència universitària. L"alumnat motivat respon amb una més gran dedicació, cosa que comporta la integració de l"alumnat en les assignatures, millors resultats acadèmics i una millor motivació del professorat. Aquest cicle de motivació es va realimentant i va produint efectes molt positius tant en el professorat com en l"alumnat. Una consideració final és que el camí per millorar la docència a Matemàtiques és, segurament, llarg. Tot i així, les reflexions i les actuacions fetes per un nombre considerable de professors de diferents disciplines i departaments de la Facultat de Matemàtiques són experiències que segurament serviran en moltes assignatures de Matemàtiques i d"altres ensenyaments.

Càlculs en xarxes elèctriques

Càlculs en xarxes elèctriques Benseny, Antoni Les xarxes elèctriques subministren als seus usuaris energia elèctrica generada en centrals nuclears, hidroelèctriques, tèrmiques, eòliques... Aquestes xarxes són controlades per les companyies elèctriques mitjancant aplicacions informàtiques que requereixen de càlculs de diversos tipus. Amb aquest material es vol fer patent i destacar la importància de la matemàtica computacional en la posada a punt d"aplicacions informàtiques de control per regulació de xarxes elèctriques.

On the configuration of Herman rings of meromorphic functions

On the configuration of Herman rings of meromorphic functions Peter, Jörn; Fagella Rabionet, Núria We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Automatic Prediction of Facial Trait Judgments: Appearance vs. Structural Models

Automatic Prediction of Facial Trait Judgments: Appearance vs. Structural Models Rojas, Mario; Masip, David; Todorov, Alexander B.; Vitrià i Marca, Jordi Evaluating other individuals with respect to personality characteristics plays a crucial role in human relations and it is the focus of attention for research in diverse fields such as psychology and interactive computer systems. In psychology, face perception has been recognized as a key component of this evaluation system. Multiple studies suggest that observers use face information to infer personality characteristics. Interactive computer systems are trying to take advantage of these findings and apply them to increase the natural aspect of interaction and to improve the performance of interactive computer systems. Here, we experimentally test whether the automatic prediction of facial trait judgments (e.g. dominance) can be made by using the full appearance information of the face and whether a reduced representation of its structure is sufficient. We evaluate two separate approaches: a holistic representation model using the facial appearance information and a structural model constructed from the relations among facial salient points. State of the art machine learning methods are applied to a) derive a facial trait judgment model from training data and b) predict a facial trait value for any face. Furthermore, we address the issue of whether there are specific structural relations among facial points that predict perception of facial traits. Experimental results over a set of labeled data (9 different trait evaluations) and classification rules (4 rules) suggest that a) prediction of perception of facial traits is learnable by both holistic and structural approaches; b) the most reliable prediction of facial trait judgments is obtained by certain type of holistic descriptions of the face appearance; and c) for some traits such as attractiveness and extroversion, there are relationships between specific structural features and social perceptions.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates Ameur, Yacin; Ortega Cerdà, Joaquim Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{

A lower bound in Nehari's theorem on the polydisc

A lower bound in Nehari's theorem on the polydisc Ortega Cerdà, Joaquim; Seip, Kristian By theorems of Ferguson and Lacey ($d=2$) and Lacey and Terwilleger ($d>2$), Nehari's theorem is known to hold on the polydisc $\D^d$ for $d>1$, i.e., if $H_\psi$ is a bounded Hankel form on $H^2(\D^d)$ with analytic symbol $\psi$, then there is a function $\varphi$ in $L^\infty(\T^d)$ such that $\psi$ is the Riesz projection of $\varphi$. A method proposed in Helson's last paper is used to show that the constant $C_d$ in the estimate $\|\varphi\|_\infty\le C_d \|H_\psi\|$ grows at least exponentially with $d$; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive Defant, Andreas; Frerick, Leonhard; Ortega Cerdà, Joaquim; Ounaïes, Myriam; Seip, Kristian The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces Constantin, Olivia; Ortega Cerdà, Joaquim We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

On Lundh's percolation diffusion

On Lundh's percolation diffusion Carroll, Tom; O'Donovan, Julie; Ortega Cerdà, Joaquim A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Beurling-Landau's density on compact manifolds

Beurling-Landau's density on compact manifolds Ortega Cerdà, Joaquim; Pridhnani, Bharti Given a compact Riemannian manifold $M$, we consider the subspace of $L^2(M)$ generated by the eigenfunctions of the Laplacian ofeigenvalue less than $L\geq1$. This space behaves like a space of polynomials and we have an analogy with the Paley-Wiener spaces. Westudy the interpolating and Marcinkiewicz-Zygmund (M-Z) families and provide necessary conditions for sampling and interpolation in termsof the Beurling-Landau densities. As an application, we prove the equidistribution of the Fekete arrays on some compact manifolds.

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Carleson Measures and Logvinenko-Sereda sets on compact manifolds Ortega Cerdà, Joaquim; Pridhnani, Bharti Given a compact Riemannian manifold $M$ of dimension $m \geq 2$, we study the space of functions of $L^2(M)$generated by eigenfunctions ofeigenvalues less than $L \geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Sherali-Adams Relaxations and Indistinguishability in Counting Logics Atserias, Albert; Maneva, Elitza Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Reliable computation of robust response tori on the verge of breakdown

Reliable computation of robust response tori on the verge of breakdown Figueras Romero, Jordi-Lluís; Haro, Àlex We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Line search multilevel optimization as computational methods for dense optical flow

Line search multilevel optimization as computational methods for dense optical flow Kalmoun, El Mostafa; Garrido Ostermann, Luis; Caselles, Vicente We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we de- velop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional mul- tilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrec- tional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimiza- tion search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow com- putation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation.

On the computation of reducible invariant tori on a parallel computer

On the computation of reducible invariant tori on a parallel computer Jorba i Monte, Àngel; Olmedo, Estrella We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity Haro, Àlex; Llave, Rafael de la In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530&br&579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Preferred Spatial Frequencies for Human Face Processing Are Associated with Optimal Class Discrimination in the Machine

Preferred Spatial Frequencies for Human Face Processing Are Associated with Optimal Class Discrimination in the Machine Keil, Matthias S.; Lapedriza i Garcia, Àgata; Masip, David; Vitrià i Marca, Jordi Psychophysical studies suggest that humans preferentially use a narrow band of low spatial frequencies for face recognition. Here we asked whether artificial face recognition systems have an improved recognition performance at the same spatial frequencies as humans. To this end, we estimated recognition performance over a large database of face images by computing three discriminability measures: Fisher Linear Discriminant Analysis, Non-Parametric Discriminant Analysis, and Mutual Information. In order to address frequency dependence, discriminabilities were measured as a function of (filtered) image size. All three measures revealed a maximum at the same image sizes, where the spatial frequency content corresponds to the psychophysical found frequencies. Our results therefore support the notion that the critical band of spatial frequencies for face recognition in humans and machines follows from inherent properties of face images, and that the use of these frequencies is associated with optimal face recognition performance.

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$ Massaneda Clares, Francesc Xavier; Ortega Cerdà, Joaquim; Ounaïes, Miriam We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Connections between signal processing and complex analysis

Connections between signal processing and complex analysis Bruna, Joaquim; Massaneda Clares, Francesc Xavier; Ortega Cerdà, Joaquim We describe one of the research lines of the Grup de Teoria de Funcions de la UAB UB, which deals with sampling and interpolation problems in signal analysis and their connections with complex function theory.

Mathematics in Catalonia: 1996-2002

Mathematics in Catalonia: 1996-2002 Cufí, Julià, 1945-; Gómez Muntané, Gerardo; Guasp Balaguer, Gregori; Reventós i Tarrida, Agustí; Serra Albó, Oriol The aim of this article is to present the main conclusions of the Report on research in Catalonia for the area of mathematics**. The report was prepared by Joaquim Bruna, Marta Sanz, Joan de Solà-Morales and the author of this text, and published by the Institute for Catalan Studies in 1998. In the report, scientific activity in the area of mathematics was measured essentially by examining two parameters: papers published in specialised journals and doctoral theses read. It should be recognised that a considerable amount of activity in the field of mathematics consists of applying existing knowledge to the resolution of practical technological problems that arise in particular companies. This kind of scientific activity was not measured in any way in the report due to the difficulty of obtaining objective data. This article is divided into the following sections: human resources, scientific production, funding, research publications, research centres, and conclusions.

Analytic behavior of the QED polarizability function at finite temperature

Analytic behavior of the QED polarizability function at finite temperature Bernal Serrano, Antonio; Pérez, Armando We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

Strange nonchaotic attractors in Harper maps

Strange nonchaotic attractors in Harper maps Haro, Àlex; Puig i Sadurní, Joaquim We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Manifolds on the verge of a hyperbolicity breakdown

Manifolds on the verge of a hyperbolicity breakdown Haro, Àlex; Llave, Rafael de la We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.

Stable heteroclinic cycles and symbolic dynamics

Stable heteroclinic cycles and symbolic dynamics Alsedà i Soler, Lluís; Gambaudo, Jean-Marc; Mumbrú i Rodriguez, Pere

A fully-automatic caudate nucleus segmentation of brain MRI: application in volumetric analysis of pediatric attention-deficit/hyperactivity disorder

A fully-automatic caudate nucleus segmentation of brain MRI: application in volumetric analysis of pediatric attention-deficit/hyperactivity disorder Igual, Laura; Soliva, Joan Carles; Hernandez-Vela, Antonio; Escalera Guerrero, Sergio; Jimenez, Xavier; Vilarroya Oliver, Óscar; Radeva, Petia Background Accurate automatic segmentation of the caudate nucleus in magnetic resonance images (MRI) of the brain is of great interest in the analysis of developmental disorders. Segmentation methods based on a single atlas or on multiple atlases have been shown to suitably localize caudate structure. However, the atlas prior information may not represent the structure of interest correctly. It may therefore be useful to introduce a more flexible technique for accurate segmentations. Method We present Cau-dateCut: a new fully-automatic method of segmenting the caudate nucleus in MRI. CaudateCut combines an atlas-based segmentation strategy with the Graph Cut energy-minimization framework. We adapt the Graph Cut model to make it suitable for segmenting small, low-contrast structures, such as the caudate nucleus, by defining new energy function data and boundary potentials. In particular, we exploit information concerning the intensity and geometry, and we add supervised energies based on contextual brain structures. Furthermore, we reinforce boundary detection using a new multi-scale edgeness measure. Results We apply the novel CaudateCut method to the segmentation of the caudate nucleus to a new set of 39 pediatric attention-deficit/hyperactivity disorder (ADHD) patients and 40 control children, as well as to a public database of 18 subjects. We evaluate the quality of the segmentation using several volumetric and voxel by voxel measures. Our results show improved performance in terms of segmentation compared to state-of-the-art approaches, obtaining a mean overlap of 80.75%. Moreover, we present a quantitative volumetric analysis of caudate abnormalities in pediatric ADHD, the results of which show strong correlation with expert manual analysis. Conclusion CaudateCut generates segmentation results that are comparable to gold-standard segmentations and which are reliable in the analysis of differentiating neuroanatomical abnormalities between healthy controls and pediatric ADHD.

Organisational adaptation of multi-agent systems in a peer-to-peer scenario

Organisational adaptation of multi-agent systems in a peer-to-peer scenario Campos Miralles, Jordi; Esteva, Marc; López Sánchez, Maite; Morales Matamoros, Javier; Salamó Llorente, Maria Organisations in Multi-Agent Systems (MAS) have proven to be successful in regulating agent societies. Nevertheless, changes in agents' behaviour or in the dynamics of the environment may lead to a poor fulfilment of the system's purposes, and so the entire organisation needs to be adapted. In this paper we focus on endowing the organisation with adaptation capabilities, instead of expecting agents to be capable of adapting the organisation by themselves. We regard this organisational adaptation as an assisting service provided by what we call the Assistance Layer. Our generic Two Level Assisted MAS Architecture (2-LAMA) incorporates such a layer. We empirically evaluate this approach by means of an agent-based simulator we have developed for the P2P sharing network domain. This simulator implements 2-LAMA architecture and supports the comparison between different adaptation methods, as well as, with the standard BitTorrent protocol. In particular, we present two alternatives to perform norm adaptation and one method to adapt agents'relationships. The results show improved performance and demonstrate that the cost of introducing an additional layer in charge of the system's adaptation is lower than its benefits.

"Dualidad de Köthe y funciones analíticas"

"Dualidad de Köthe y funciones analíticas" Cerdà Martín, Joan Lluís

Extrapolation theory for the real interpolation method

Extrapolation theory for the real interpolation method Carro Rossell, María Jesús; Martín i Pedret, Joaquim We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega