Vector Calculus on weighted networks

In this work we study the different type of regular boundary value problems on a path associated with the Schr\"odinger operator. In particular, we get the Poisson kernel and the Green function for each problem and we emphasize the cases of Dirichlet, Neumann, Mixed and periodic problems. In any case, the Poisson kernel and the Green function are given in terms of second and third kind Chebyshev polynomials since they verify a recurrence law similar to the one verified by the Sch\"odinger operator on a path.

Country

Spain

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Keywords

Difference equations, Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::39 Difference and functional equations ::39A Difference equations {For dynamical systems, see 37-xx}, :Matemàtiques i estadística [Àrees temàtiques de la UPC], Equacions diferencials, Discrete operators, Anàlisi vectorial, see 37-xx}, Differential calculus, Classificació AMS::39 Difference and functional equations ::39A Difference equations {For dynamical systems, Network cohomology, Discrete green identity, Vector calculus, :39 Difference and functional equations ::39A Difference equations {For dynamical systems, see 37-xx} [Classificació AMS]

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