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WKB eigenmode construction for analytic Toeplitz operators

Alix Deleporte

Vol. 5 (2023), No. 2, 213–260
Abstract

We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of nondegenerate wells. These quasimodes follow the WKB ansatz; the error is O(ecN), where c > 0 and N + is the inverse semiclassical parameter.

Keywords
semiclassical, Berezin–Toeplitz, Toeplitz, analytic, spectral theory, WKB
Mathematical Subject Classification
Primary: 32A25, 35A20, 35P10, 35Q40, 81Q20
Secondary: 32W50, 58J40, 58J50
Milestones
Received: 13 July 2021
Revised: 19 April 2022
Accepted: 26 August 2022
Published: 26 June 2023
Authors
Alix Deleporte
Université de Strasbourg, CNRS, IRMA UMR 7501, F-67000
Strasbourg, France
Institut für Mathematik
Universität Zürich, Zürich
Université Paris-Saclay, CNRS
Laboratoire de mathématiques d’Orsay, F-91405
Orsay
France