Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy

M. Burak Erdoǧan, William R. Green

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate L1(ℝ2) → L(ℝ2) dispersive estimates for the Schrödinger operator H = -Δ+V when there are obstructions, resonances or an eigenvalue, at zero energy. In particular, we show that the existence of an s-wave resonance at zero energy does not destroy the t-1 decay rate. We also show that if there is a p-wave resonance or an eigenvalue at zero energy, then there is a time dependent operator Ft satisfying. We also establish a weighted dispersive estimate with t-1 decay rate in the case when there is an eigenvalue at zero energy but no resonances.

Original languageEnglish (US)
Pages (from-to)6403-6440
Number of pages38
JournalTransactions of the American Mathematical Society
Volume365
Issue number12
DOIs
StatePublished - 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy'. Together they form a unique fingerprint.

Cite this