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

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