The Lp-continuity of wave operators for higher order Schrödinger operators

M. Burak Erdoğan, William R. Green

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the higher order Schrödinger operator H=(−Δ)m+V(x) in n dimensions with real-valued potential V when n>2m, m∈N, m>1. When n is odd, we prove that the wave operators extend to bounded operators on Lp(Rn) for all 1≤p≤∞ under n and m dependent conditions on the potential analogous to the case when m=1. Further, if V is small in certain norms, that depend n and m, the wave operators are bounded on the same range for even n. We further show that if the smallness assumption is removed in even dimensions the wave operators remain bounded in the range 1<p<∞.

Original languageEnglish (US)
Article number108450
JournalAdvances in Mathematics
Volume404
DOIs
StatePublished - Aug 6 2022

Keywords

  • Higher order Schrödinger
  • Wave operator

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'The Lp-continuity of wave operators for higher order Schrödinger operators'. Together they form a unique fingerprint.

Cite this