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Regular boundary value problems on a path throughout Chebyshev Polynomials
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
In this work we study the different types of regular boundary valueproblems on a path associated with the Schrödinger operator. Inparticular, we obtain the Green function for each problem and weemphasize the case of Sturm-Liouville boundary conditions. Inaddition, we study the periodic boundary value problem thatcorresponds to the Poisson equation in a cycle. In any case, theGreen functions are given in terms of Chebyshev polynomials sincethey verify a recurrence law similar to the one verified by theSchrödinger operator on a path.
2012-05-10
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
Boundary value problems
Chebyshev polynomials
Discrete Schrödinger operator
boundary value problems
paths
Chebyshev polynomials
Green functions
Chebyshev, Polinomis de
Problemes extrems (Matemàtica)
/Classificació AMS/34 Ordinary differential equations/34B Boundary value problems {For ordinary differential operators, see 34Lxx}
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