Norm-ideal perturbations of one-parameter semigroups and applications

Lyonell Boulton, Spyridon Dimoudis

Research output: Contribution to journalArticlepeer-review

5 Downloads (Pure)

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.
Original languageEnglish
Article number109784
JournalJournal of Functional Analysis
Volume284
Issue number4
Early online date23 Nov 2022
DOIs
Publication statusE-pub ahead of print - 23 Nov 2022

Keywords

  • Dyson–Phillips expansion
  • Non-self-adjoint Schrödinger operators
  • Perturbation of one-parameter semigroups
  • Schatten–von Neumann ideals

ASJC Scopus subject areas

  • Analysis

Fingerprint

Dive into the research topics of 'Norm-ideal perturbations of one-parameter semigroups and applications'. Together they form a unique fingerprint.

Cite this