Poisson relation for the scattering kernel and inverse scattering by obstacles
Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995)
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topStoyanov, L.. "Poisson relation for the scattering kernel and inverse scattering by obstacles." Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995): 1-10. <http://eudml.org/doc/112116>.
@article{Stoyanov1994-1995,
author = {Stoyanov, L.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectral geometry; inverse obstacle scattering; geometric scattering theory},
language = {eng},
pages = {1-10},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Poisson relation for the scattering kernel and inverse scattering by obstacles},
url = {http://eudml.org/doc/112116},
year = {1994-1995},
}
TY - JOUR
AU - Stoyanov, L.
TI - Poisson relation for the scattering kernel and inverse scattering by obstacles
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1994-1995
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 10
LA - eng
KW - spectral geometry; inverse obstacle scattering; geometric scattering theory
UR - http://eudml.org/doc/112116
ER -
References
top- [G] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix, Publ. RIMS Kyoto Univ.12 (1977), 69-88. Zbl0381.35064MR448453
- [GM] V. Guillemin and R. Melrose, The Poisson sumation formula for manifolds with boundary, Adv. in Math.32 (1979), 204-232. Zbl0421.35082MR539531
- [H] L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. III, Berlin, Springer, 1985. Zbl1115.35005
- [LP1] P. Lax and R. Phillips, Scattering Theory, Academic Press, New York, 1967. Zbl0186.16301MR217440
- [LP2] P. Lax and R. Phillips, The scattering of sound waves by an obstacle, Comm. Pure Appl. Math.30 (1977), 195-233. Zbl0335.35075MR442510
- [Ma] A. Majda, A representation formula for the scattering operator and the inverse problem for arbitrary bodies, Comm. Pure Appl. Math.30 (1977), 165-194. Zbl0335.35076MR435625
- [MaT] A. Majda and M. Taylor, Inverse scattering problems for transparant obstacles, electromagnetic waves and hyperbolic systems, Commun. Partial Diff. Equations2 (1977), 395-438. Zbl0373.35055MR437946
- [M1] R. Melrose, Microlocal parametrices for diffractive boundary value problems, Duke Math. J.42 (1975), 605-635. Zbl0368.35055MR517101
- [M2] R. Melrose, Equivalence of glancing hypersurfaces, Invent. Math.37, 165-191 (1976) Zbl0354.53033MR436225
- [M3] R. Melrose, Geometric Scattering Theory, Lectures at Stanford University, M.I.T.1994. Zbl0849.58071MR1350074
- [MS] R. Melrose and J. Sjöstrand, Singularities in boundary value problems. I, II. Comm. Pure Appl. Math.31 (1978), 593-617; 35 (1982),129-168. Zbl0546.35083
- [P] V. Petkov, High frequency asymptotics of the scattering amplitude for non-convex bodies. Commun. Partial Diff. Equations5 (1980), 293-329. Zbl0435.35065MR562545
- [PS1] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, John Wiley & Sons, Chichester, 1992. Zbl0761.35077MR1172998
- [PS2] V. Petkov and L. Stoyanov, Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian, Ann. Inst. Henri Poincare (Physique Theorique), to appear. Zbl0838.35093MR1313359
- [So] H. Soga, Singularities of the scattering kernel for convex obstacles, J. Math. Kyoto Univ.22 (1983), 729-765. Zbl0511.35070MR685528
- [St1] L. Stoyanov, Regularity properties of the generalized Hamiltonian flow, Seminaire EDP, Ecole Polytechnique, Exposé, 1992 -1993. Zbl0881.58028MR1240547
- [St2] L. Stoyanov, Generalized Hamiltonian flow and Poisson relation for the scattering kernel, Preprint, Maths. Dept., University of Western Australia1994.
- [T] M. Taylor, Grazing rays and reflection of singularities to wave equations, Commun. Pure Appl. Math.29 (1978), 1-38. Zbl0318.35009MR397175
- [Y] K. Yamamoto, Characterization of a convex obstacle by singularities of the scattering kernel, J. Diff. Equations64 (1986), 283-293. Zbl0611.35066MR857711
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