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Published April 2015 | Published + Submitted
Journal Article Open

Trace Class Conditions for Functions of Schrödinger Operators

Abstract

We consider the difference f(−Δ+V)−f(−Δ) of functions of Schrödinger operators in L^2(R^d) and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions f and in V belonging only to some L^p space. This is motivated by applications in mathematical physics related to Lieb–Thirring inequalities. We show that in the particular case of Schrödinger operators the well-known sufficient conditions on f, based on a general operator theoretic result due to V. Peller, can be considerably relaxed. We prove similar theorems for f(−Δ+V)−f(−Δ)−^d/_(dα)f(−Δ+αV)|α=0 . Our key idea is the use of the limiting absorption principle.

Additional Information

© 2014 The Author(s). Copyright © 2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 4 February 2014. Accepted: 26 May 2014. Published online: 6 November 2014. Communicated by L. Erdös. The authors are grateful to M. Lewin, J. Sabin and D. Yafaev for useful discussions. Financial support from the U.S. National Science Foundation through Grant PHY-1347399 (R. F.) is acknowledged.

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Published - art_10.1007_s00220-014-2205-8.pdf

Submitted - 1402.0763v1.pdf

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August 20, 2023
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