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Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in $ {\bf R}\sp 3$


Author: Luchezar Stojanov
Journal: Proc. Amer. Math. Soc. 113 (1991), 847-856
MSC: Primary 58G25; Secondary 35L05, 35P25
DOI: https://doi.org/10.1090/S0002-9939-1991-1070532-9
MathSciNet review: 1070532
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Abstract: It is proved for fixed unit vectors $ \omega \ne \theta $ in $ {\mathbb{R}^3}$ and generic bounded open domains $ \mathfrak{D} \subset {\mathbb{R}^3}$ that there do not exist generalized $ (\omega ,\theta )$-rays in $ \Omega = {\mathbb{R}^3}\backslash \mathfrak{D}$ containing nontrivial geodesies on $ \partial \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 )$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1070532-9
Keywords: Generalized and reflecting $ (\omega ,\theta )$-rays, sojourn time, scattering kernel, generic
Article copyright: © Copyright 1991 American Mathematical Society

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