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Counting eigenvalues of Schrödinger operators with fast decaying complex potentials

Borichev, Alexander and Frank, Rupert L. and Volberg, Alexander (2022) Counting eigenvalues of Schrödinger operators with fast decaying complex potentials. Advances in Mathematics, 397 . Art. No. 108115. ISSN 0001-8708. doi:10.1016/j.aim.2021.108115.

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We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman–Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schrödinger operators with rapidly decreasing complex-valued potentials, and, more generally, for non-symmetric Jacobi matrices.

Item Type:Article
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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2021 Elsevier. Received 14 August 2020, Revised 14 September 2021, Accepted 3 October 2021, Available online 25 November 2021. The second and third author acknowledge partial support by the U.S. National Science Foundation through grants DMS-1363432, DMS-1954995 (R.L.F.) and DMS-1600065 (A.V.). This paper is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the second and the third author were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester. The first and the third authors were partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
Funding AgencyGrant Number
Simons Foundation346300
Ministerstwo Nauki i Szkolnictwa Wyższego (MNiSW)UNSPECIFIED
Subject Keywords:Nonselfadjoint operator; Schrödinger operators; Eigenvalues; Quasianalyticity; Zeros of analytic functions
Classification Code:MSC: 42B20; 42B35; 47A30
Record Number:CaltechAUTHORS:20211202-191328270
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Official Citation:Alexander Borichev, Rupert L. Frank, Alexander Volberg, Counting eigenvalues of Schrödinger operators with fast decaying complex potentials, Advances in Mathematics, Volume 397, 2022, 108115, ISSN 0001-8708,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112175
Deposited By: George Porter
Deposited On:02 Dec 2021 22:32
Last Modified:15 Feb 2022 20:36

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