Non-self-adjoint operators, infinite determinants, and some applications
Abstract
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a variant of the Birman-Schwinger principle as well as local and global Weinstein-Aronszajn formulas. Our applications include a study of suitably symmetrized (modified) perturbation determinants of Schr\"odinger operators in dimensions n=1,2,3 and their connection with Krein's spectral shift function in two- and three-dimensional scattering theory. Moreover, we study an appropriate multi-dimensional analog of the celebrated formula by Jost and Pais that identifies Jost functions with suitable Fredholm (perturbation) determinants and hence reduces the latter to simple Wronski determinants.
Cite
@article{arxiv.math/0511371,
title = {Non-self-adjoint operators, infinite determinants, and some applications},
author = {Fritz Gesztesy and Yuri Latushkin and Marius Mitrea and Maxim Zinchenko},
journal= {arXiv preprint arXiv:math/0511371},
year = {2020}
}
Comments
41 pages, hypotheses and proof of Theorem 4.5 got corrected