Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in $\textbf {R}^ 3$
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- by Luchezar Stojanov PDF
- Proc. Amer. Math. Soc. 113 (1991), 847-856 Request permission
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 $s(t,\theta ,\omega )$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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