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Vector Calculus on weighted networks
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
In this work we study the different type of regular boundary valueproblems on a path associated with the Schr\"odinger operator. Inparticular, we get the Poisson kernel and the Green function foreach problem and we emphasize the cases of Dirichlet, Neumann, Mixedand periodic problems. In any case, the Poisson kernel and the Greenfunction are given in terms of second and third kind Chebyshevpolynomials since they verify a recurrence law similar to the oneverified by the Sch\"odinger operator on a path.
2012-05-10
Àrees temàtiques de la UPC::Matemàtiques i estadística
Difference equations
Differential calculus
Discrete operators
Discrete green identity
Vector calculus
Network cohomology
Equacions diferencials
Anàlisi vectorial
/Classificació AMS/39 Difference and functional equations /39A Difference equations {For dynamical systems, see 37-xx}
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