PreprintCC BY 4.0arXiv
An optimization problem for δ' leaky stars
Abstract
We consider singular Schrödinger operators with an attractive δ' interaction of strength β supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of the maximum symmetry. Two different proofs are presented, one for an even number of edges using a comparison to the δ interaction star, the other general based on Birman-Schwinger technique.
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BibTeX
@misc{exner2026optimization,
title = {{An optimization problem for $δ'$ leaky stars}},
author = {Pavel Exner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15771},
eprint = {2610.15771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15771},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An optimization problem for δ' leaky stars
AU - Pavel Exner
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15771
UR - https://arxiv.org/abs/2610.15771
AB - We consider singular Schrödinger operators with an attractive δ' interaction of strength β supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of the maximum symmetry. Two different proofs are presented, one for an even number of edges using a comparison to the δ interaction star, the other general based on Birman-Schwinger technique.
ER -