NONEXISTENCE OF GENERALIZED SCATTERING RAYS AND SINGULARITIES OF THE SCATTERING KERNEL FOR GENERIC DOMAINS IN R3

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Abstract

It is proved for fixed unit vectors-omega not-equal theta in R3 and generic bounded open domains D subset-of R3 that there do not exist generalized (omega, theta)-rays in OMEGA = R3\D containing nontrivial geodesics on partial derivative-OMEGA. Consequently, for generic domains the sojourn times of reflecting (omega, theta)-rays completely describe the set of singularities of the scattering kernel s(t, theta, omega).

Original languageEnglish
Pages (from-to)847-856
Number of pages10
JournalProceedings of the American Mathematical Society
Volume113
Issue number3
DOIs
Publication statusPublished - Nov 1991

Cite this

@article{e8216e11759b471c8e2222a0db1392ec,
title = "NONEXISTENCE OF GENERALIZED SCATTERING RAYS AND SINGULARITIES OF THE SCATTERING KERNEL FOR GENERIC DOMAINS IN R3",
abstract = "It is proved for fixed unit vectors-omega not-equal theta in R3 and generic bounded open domains D subset-of R3 that there do not exist generalized (omega, theta)-rays in OMEGA = R3\D containing nontrivial geodesics on partial derivative-OMEGA. Consequently, for generic domains the sojourn times of reflecting (omega, theta)-rays completely describe the set of singularities of the scattering kernel s(t, theta, omega).",
keywords = "GENERALIZED AND REFLECTING (OMEGA,THETA)-RAYS, SOJOURN TIME, SCATTERING KERNEL, GENERIC",
author = "L. Stoyanov",
year = "1991",
month = "11",
doi = "10.2307/2048623",
language = "English",
volume = "113",
pages = "847--856",
journal = "Proceedings of the American Mathematical Soceity",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "3",

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AU - Stoyanov, L.

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N2 - It is proved for fixed unit vectors-omega not-equal theta in R3 and generic bounded open domains D subset-of R3 that there do not exist generalized (omega, theta)-rays in OMEGA = R3\D containing nontrivial geodesics on partial derivative-OMEGA. Consequently, for generic domains the sojourn times of reflecting (omega, theta)-rays completely describe the set of singularities of the scattering kernel s(t, theta, omega).

AB - It is proved for fixed unit vectors-omega not-equal theta in R3 and generic bounded open domains D subset-of R3 that there do not exist generalized (omega, theta)-rays in OMEGA = R3\D containing nontrivial geodesics on partial derivative-OMEGA. Consequently, for generic domains the sojourn times of reflecting (omega, theta)-rays completely describe the set of singularities of the scattering kernel s(t, theta, omega).

KW - GENERALIZED AND REFLECTING (OMEGA,THETA)-RAYS

KW - SOJOURN TIME

KW - SCATTERING KERNEL

KW - GENERIC

U2 - 10.2307/2048623

DO - 10.2307/2048623

M3 - Article

VL - 113

SP - 847

EP - 856

JO - Proceedings of the American Mathematical Soceity

JF - Proceedings of the American Mathematical Soceity

SN - 0002-9939

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ER -