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Trace Class Conditions for Functions of Schrödinger Operators

Frank, Rupert L. and Pushnitski, Alexander (2015) Trace Class Conditions for Functions of Schrödinger Operators. Communications in Mathematical Physics, 335 (1). pp. 477-496. ISSN 0010-3616. doi:10.1007/s00220-014-2205-8. https://resolver.caltech.edu/CaltechAUTHORS:20150330-070612488

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00220-014-2205-8DOIArticle
http://link.springer.com/article/10.1007/s00220-014-2205-8PublisherArticle
http://arxiv.org/abs/1402.0763arXivDiscussion Paper
http://rdcu.be/rF5dPublisherFree ReadCube access
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
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.
Funders:
Funding AgencyGrant Number
NSFPHY-1347399
Issue or Number:1
DOI:10.1007/s00220-014-2205-8
Record Number:CaltechAUTHORS:20150330-070612488
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150330-070612488
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56199
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 Mar 2015 16:14
Last Modified:10 Nov 2021 20:56

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