The spectral $ζ$-function of Sturm--Liouville operators with $N$ generalized point potentials
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fucci, Guglielmo, Stanfill, Jonathan
Institutions: East Carolina University, The Ohio State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213585956