Scattering for Schrödinger operators in a class of domains with non-compact boundaries

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Abstract

Schrödinger operators in a class of domains with asymptotic cones are considered. A generalized Fourier transform representing the absolutely continuous part of the Schrödinger operator as multiplication by |ξ|2 in the asymptotic cone is constructed. Wave operators relating the free Laplacian to Schrödinger operators are computed using the generalized Fourier transform. The wave operators relating Schrödinger operators acting in domains with the same asymptotic cone are computed and shown to be complete.

Original languageEnglish (US)
Pages (from-to)87-119
Number of pages33
JournalJournal of Functional Analysis
Volume44
Issue number1
DOIs
StatePublished - Oct 15 1981
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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