Eigenvalues with respect to a weight for general boundary value problems on networks
In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is positive semi-definite on the space of functions satisfying the null boundary co...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/336840 |
| Acceso en línea: | https://hdl.handle.net/2117/336840 https://dx.doi.org/10.1016/j.laa.2020.03.046 |
| Access Level: | acceso abierto |
| Palabra clave: | Schrödinger operators Eigenvalues Green operators Positive semi-definiteness Discrete trace Mercer theorem Classificació AMS::39 Difference and functional equations::39A Difference equations Classificació AMS::34 Ordinary differential equations::34B Boundary value problems Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::16 Associative rings and algebras Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is positive semi-definite on the space of functions satisfying the null boundary conditions. To do this, the fundamental tools are the Doob transform and the discrete version of the trace function. Then, we raise eigenvalue problems with respect to a weight for general boundary value problems and we prove the discrete version of the Mercer Theorem. Finally, we apply the obtained results to a Dirichlet-Robin boundary value problem on a star-like network. |
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