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Schatten Class Conditions for Functions of Schrödinger Operators

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Rupert L. Frank, Alexander Pushnitski

Original languageEnglish
Pages (from-to)3543-3562
Number of pages20
JournalAnnales Henri Poincare
Issue number11
Published1 Nov 2019

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We consider the difference f(H1) - f(H) , where H= - 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.

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