The spectral ζ-function of Sturm--Liouville operators with N generalized point potentials
Abstract
This work analyzes the spectral zeta function associated with regular and singular Sturm--Liouville operators endowed with N generalized point potentials. The point interactions are characterized as a particular class of self-adjoint extensions of Sturm--Liouville operators defined on a chain of N+1 adjacent intervals. Each interaction is described by SL(2,R) matching conditions relating generalized boundary values across neighboring intervals. We construct the spectral zeta function associated with Sturm--Liouville operators endowed with N generalized point potentials in terms of a contour integral involving an appropriate characteristic function. The process of analytic continuation of the spectral zeta function to a neighborhood of the origin is illustrated by means of specific examples where the ζ-regularized functional determinant is also explicitly computed.
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BibTeX
@misc{fucci2026spectral,
title = {{The spectral $ζ$-function of Sturm--Liouville operators with $N$ generalized point potentials}},
author = {Guglielmo Fucci and Jonathan Stanfill},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19322},
eprint = {2609.19322},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19322},
}
RIS
TY - UNPB
TI - The spectral ζ-function of Sturm--Liouville operators with N generalized point potentials
AU - Guglielmo Fucci
AU - Jonathan Stanfill
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19322
UR - https://arxiv.org/abs/2609.19322
AB - This work analyzes the spectral zeta function associated with regular and singular Sturm--Liouville operators endowed with N generalized point potentials. The point interactions are characterized as a particular class of self-adjoint extensions of Sturm--Liouville operators defined on a chain of N+1 adjacent intervals. Each interaction is described by SL(2,R) matching conditions relating generalized boundary values across neighboring intervals. We construct the spectral zeta function associated with Sturm--Liouville operators endowed with N generalized point potentials in terms of a contour integral involving an appropriate characteristic function. The process of analytic continuation of the spectral zeta function to a neighborhood of the origin is illustrated by means of specific examples where the ζ-regularized functional determinant is also explicitly computed.
ER -