Norm-ideal perturbations of one-parameter semigroups and applications
Abstract
The notion of equivalence classes of generators of one-parameter semigroups based on the convergence of the Dyson expansion can be traced back to the seminal work of Hille and Phillips, who in Chapter XIII of the 1957 edition of their Functional Analysis monograph, developed the theory in minute detail. Following their approach of regarding the Dyson expansion as a central object, in the first part of this paper we examine a general framework for perturbation of generators relative to the Schatten-von Neumann ideals on Hilbert spaces. This allows us to develop a graded family of equivalence relations on generators, which refine the classical notion and provide stronger-than-expected properties of convergence for the tail of the perturbation series. We then show how this framework realises in the context of non-self-adjoint Schrödinger operators.
Citation
Boulton , L & Dimoudis , S 2023 , ' Norm-ideal perturbations of one-parameter semigroups and applications ' , Journal of Functional Analysis , vol. 284 , no. 4 , 109784 . https://doi.org/10.1016/j.jfa.2022.109784
Publication
Journal of Functional Analysis
Status
Peer reviewed
ISSN
0022-1236Type
Journal article
Description
Funding: SD was supported by Heriot-Watt University's James Watt scholarships programme.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.