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

Peter Constantin

doi:10.1016/0022-1236(81)90006-9

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

Peter Constantin

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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 language	English (US)
Pages (from-to)	87-119
Number of pages	33
Journal	Journal of Functional Analysis
Volume	44
Issue number	1
DOIs	https://doi.org/10.1016/0022-1236(81)90006-9
State	Published - Oct 15 1981
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/0022-1236(81)90006-9

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title = "Scattering for Schr{\"o}dinger operators in a class of domains with non-compact boundaries",

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

author = "Peter Constantin",

year = "1981",

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doi = "10.1016/0022-1236(81)90006-9",

language = "English (US)",

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PY - 1981/10/15

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N2 - 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.

AB - 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.

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U2 - 10.1016/0022-1236(81)90006-9

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EP - 119

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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

Abstract

All Science Journal Classification (ASJC) codes

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