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

L. Stoyanov

doi:10.2307/2048623

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

L. Stoyanov

School of Physics, Mathematics and Computing

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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 language	English
Pages (from-to)	847-856
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	113
Issue number	3
DOIs	https://doi.org/10.2307/2048623
Publication status	Published - Nov 1991

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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\textbackslash{}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 = nov,

doi = "10.2307/2048623",

language = "English",

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journal = "Proceedings of the American Mathematical Society",

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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

SN - 0002-9939

VL - 113

SP - 847

EP - 856

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

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

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