Arkiv för Matematik

Volume 59 (2021)

Number 2

Resonances over a potential well in an island

Pages: 385 – 437

DOI: https://dx.doi.org/10.4310/ARKIV.2021.v59.n2.a7

Authors

Johannes Sjöstrand (Institut de Mathématiques de Bourgogne, Université de Bourgogne Franche-Comté, Dijon, France)

Maher Zerzeri (Laboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris-Nord, Villetaneuse, France)

Abstract

In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.

Keywords

resonances, semi-classical asymptotic, microlocal analysis, Schrödinger operator, potential well, maximal energy

2010 Mathematics Subject Classification

Primary 35J10. Secondary 35B34, 35P20, 47A55.

Received 10 April 2020

Received revised 10 December 2020

Accepted 28 December 2020

Published 11 November 2021