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Schatten class conditions for functions of Schrödinger operators

Frank, Rupert L. and Pushnitski, Alexander (2019) Schatten class conditions for functions of Schrödinger operators. Annales Henri Poincaré, 20 (11). pp. 3543-3562. ISSN 1424-0637. https://resolver.caltech.edu/CaltechAUTHORS:20190520-133945892

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Abstract

We consider the difference f(H_1)−f(H_0), where H_0 = −Δ and H_1 = −Δ+V are the free and the perturbed Schrödinger operators in L^2(R^d), and V is a real-valued short range potential. We give a sharp sufficient condition for this difference to belong to a given Schatten class S_p, 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00023-019-00838-8DOIArticle
https://arxiv.org/abs/1901.05789arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2019 Springer Nature Switzerland AG. First Online: 09 September 2019. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.) is acknowledged. A.P. is grateful to Caltech for hospitality.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Issue or Number:11
Record Number:CaltechAUTHORS:20190520-133945892
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190520-133945892
Official Citation:Frank, R.L. & Pushnitski, A. Ann. Henri Poincaré (2019) 20: 3543. https://doi.org/10.1007/s00023-019-00838-8
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95607
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 May 2019 20:54
Last Modified:22 Oct 2019 22:01

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