Eigenvalue bounds for Schrödinger operators with complex potentials. III

Frank, Rupert L. (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. III. Transactions of the American Mathematical Society, 370 . pp. 219-240. ISSN 0002-9947. https://resolver.caltech.edu/CaltechAUTHORS:20170502-081943954

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Abstract

We discuss the eigenvalues E_j of Schrödinger operators −Δ+V in L^2(R^d) with complex potentials V ∈ L^p, p < ∞. We show that (A) Re E_j → ∞ implies Im E_j → 0, and (B) Re E_j → E ∈ [0,∞) implies (Im E_j) ∈ ℓ^q for some q depending on p. We prove quantitative versions of (A) and (B) in terms of the L^p-norm of V.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1090/tran/6936	DOI	Article
http://www.ams.org/journals/tran/2018-370-01/S0002-9947-2017-06936-1	Publisher	Article
https://arxiv.org/abs/1510.03411	arXiv	Discussion Paper

ORCID:

Author	ORCID
Frank, Rupert L.	0000-0001-7973-4688

Additional Information:

© 2017 by the Author. Received by the editors October 12, 2015 and, in revised form, March 14, 2016. Published electronically: July 13, 2017. The author was supported by NSF grant DMS-1363432. Fundamental for several of the new theorems here are results from [13], which were obtained jointly with J. Sabin to whom the author is most grateful. He would also like to thank M. Demuth and M. Hansmann for fruitful discussions and M. Demuth, L. Golinskii and F. Hanauska for helpful remarks on a previous version of this manuscript. This paper has its origin at the conference “Mathematical aspects of physics with non-self-adjoint operators” in June 2015 and the author is grateful to the organizers and the American Institute of Mathematics for the invitation. This paper was finished at the Mittag–Leffler Institute and the author is grateful to A. Laptev for the hospitality.

Funders:

Funding Agency	Grant Number
NSF	DMS-1363432

Classification Code:

2010 Mathematics Subject Classification: Primary 35P15, 31Q12

Record Number:

CaltechAUTHORS:20170502-081943954

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170502-081943954

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No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

77119

Collection:

CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

02 May 2017 18:02

Last Modified:

09 Mar 2020 13:18

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