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Eigenvalues with respect to a weight for general boundary value problems on networks

Author
Carmona, A.; Encinas, A.; Mitjana, M.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2021-04-01
Volume
614
First page
208
Last page
243
DOI
10.1016/j.laa.2020.03.046
Repository
http://hdl.handle.net/2117/336840 Open in new window
URL
https://www.sciencedirect.com/science/article/abs/pii/S0024379520301816 Open in new window
Abstract
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 val...
Citation
Carmona, A.; Encinas, A.; Mitjana, M. Eigenvalues with respect to a weight for general boundary value problems on networks. "Linear algebra and its applications", 1 Abril 2021, vol. 614, p. 208-243.
Keywords
Discrete trace, Eigenvalues, Green operators, Mercer theorem, Positive semi-definiteness, Schrödinger operators
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory