Schatten class conditions for functions of Schrodinger operators

Rupert L. Frank*, Alexander Pushnitski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
88 Downloads (Pure)

Abstract

We consider the difference f(H1)−f(H0), where H0=−Δ and H1=−Δ+V are the free and the perturbed Schrödinger operators in L2(Rd), respectively, in which V is a real-valued short range potential. We give a sufficient condition for this difference to belong to a given Schatten class Sp, depending on the rate of decay of the potential and on the smoothness of f (stated in terms of the membership in a Besov class). In particular, for p>1 we allow for some unbounded functions f.
Original languageEnglish
Pages (from-to)3543-3562
Number of pages20
JournalAnnales Henri Poincare
Volume20
Issue number11
Early online date29 Sept 2019
DOIs
Publication statusPublished - 1 Nov 2019

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