On a generalization of Rouché's theorem for trace ideals with applications for resonances of Schrödinger operators
type: Item
instance of: scholarly article
title: On a generalization of Rouché's theorem for trace ideals with applications for resonances of Schrödinger operators
zbMATH Open document ID: 0692.47002
DOI: 10.1016/0022-247X(89)90085-1
author: Heinz Siedentop
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let \(f(z)=1+F(z)\) be an operator-valued function meromorphic on a simply connected domain \(\Gamma\) and analytic on its boundary \(\partial \Gamma\) such that F(z) belongs to the Schatten-von Neumann class \(I_ p\) with \(p\geq 1\). The behaviour under perturbation of the expression \[ N_{\Gamma}(F)=(2\pi i)^{-1}\quad trace(\oint_{\partial \Gamma}f'(z)f(z)^{-1} dz) \] is investigated. Note that, in the analytic case, \(N_{\Gamma}(F)\) counts the number of eigenvalues (-1) of F(z) in \(\Gamma\).
reviewed by: Albrecht Pietsch
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A70
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 4132933
zbMATH Keywords: trace
zbMATH Keywords: determinant
zbMATH Keywords: operator-valued function meromorphic on a simply connected domain
zbMATH Keywords: Schatten-von Neumann class
zbMATH Keywords: number of eigenvalues
MaRDI profile type: Publication
cites work: Q5514022
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description: scientific article; zbMATH DE number 4132933