Pseudomodes for Schrödinger operators with complex potentials

David Krejčiřík, Petr Siegl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For one-dimensional Schrödinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. We develop a first systematic non-semi-classical approach, which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones. Applications of the present results to higher-dimensional Schrödinger operators are also discussed.

Original languageEnglish
Pages (from-to)2856-2900
Number of pages45
JournalJournal of Functional Analysis
Volume276
Issue number9
DOIs
Publication statusPublished - 1 May 2019
Externally publishedYes

Keywords

  • Complex potential
  • Pseudospectrum
  • Schrödinger operators
  • WKB

ASJC Scopus subject areas

  • Analysis

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