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Frank, Rupert L. and Pushnitski, Alexander (2019): Schatten Class Conditions for Functions of Schrodinger Operators. In: Annales Henri Poincare, Vol. 20, No. 11: pp. 3543-3562

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Abstract

We consider the difference f(H1)- f(H0), where H0 = -. and H1 = -.+ V are the free and the perturbed Schr<spacing diaeresis>odinger 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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