Ruminations on Hejhal’s theorem about the Bergman and Szegő kernels

We give a new proof of Dennis Hejhal’s theorem on the nondegeneracy of the matrix that appears in the identity relating the Bergman and Szegő kernels of a smoothly bounded finitely connected domain in the plane. Mergelyan’s theorem is at the heart of the argument. We explore connections of Hejhal’s...

Full description

Saved in:
Bibliographic Details
Published in:Analysis and mathematical physics 2022-02, Vol.12 (1), Article 24
Main Authors: Bell, Steven R., Gustafsson, Björn
Format: Article
Language:English
Subjects:
30C40
Analysis
In memory of Harold Seymour Shapiro (1928-2021)
Kernels
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give a new proof of Dennis Hejhal’s theorem on the nondegeneracy of the matrix that appears in the identity relating the Bergman and Szegő kernels of a smoothly bounded finitely connected domain in the plane. Mergelyan’s theorem is at the heart of the argument. We explore connections of Hejhal’s theorem to properties of the zeroes of the Szegő kernel and propose some ideas to better understand Hejhal’s original theorem.
ISSN:1664-2368
1664-235X
1664-235X
DOI:10.1007/s13324-021-00634-w