Inverse Scattering for Waveguides

Hiroshi Isozaki[1]; Yaroslav Kurylev[2]; Matti Lassas[3]

  • [1] University of Tsukuba Institute of Mathematics Tsukuba, 305-8571 (Japan)
  • [2] University College of London Department of Mathematics United Kingdom
  • [3] Helsinki University of Technology Department of Mathematics Finland

Séminaire de théorie spectrale et géométrie (2006-2007)

  • Volume: 25, page 71-83
  • ISSN: 1624-5458

Abstract

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We study the inverse scattering problem for a waveguide ( M , g ) with cylindrical ends, M = M c ∪ ∪ α = 1 N ( Ω α × ( 0 , ∞ ) ) , where each Ω α × ( 0 , ∞ ) has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines ( M , g ) up to an isometry.

How to cite

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Isozaki, Hiroshi, Kurylev, Yaroslav, and Lassas, Matti. "Inverse Scattering for Waveguides." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 71-83. <http://eudml.org/doc/11231>.

@article{Isozaki2006-2007,
abstract = {We study the inverse scattering problem for a waveguide $(M, \{\bf g\})$ with cylindrical ends, $M=M^c \cup \left(\cup _\{\alpha =1\}^\{N\} (\Omega ^\{\alpha \} \times (0, \infty ))\right)$, where each $\Omega ^\{\alpha \} \times (0, \infty )$ has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines $(M, \{\bf g\})$ up to an isometry.},
affiliation = {University of Tsukuba Institute of Mathematics Tsukuba, 305-8571 (Japan); University College of London Department of Mathematics United Kingdom; Helsinki University of Technology Department of Mathematics Finland},
author = {Isozaki, Hiroshi, Kurylev, Yaroslav, Lassas, Matti},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {inverse scattering problem; Riemannian manifolds with cylindrical ends; waveguides},
language = {eng},
pages = {71-83},
publisher = {Institut Fourier},
title = {Inverse Scattering for Waveguides},
url = {http://eudml.org/doc/11231},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Isozaki, Hiroshi
AU - Kurylev, Yaroslav
AU - Lassas, Matti
TI - Inverse Scattering for Waveguides
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 71
EP - 83
AB - We study the inverse scattering problem for a waveguide $(M, {\bf g})$ with cylindrical ends, $M=M^c \cup \left(\cup _{\alpha =1}^{N} (\Omega ^{\alpha } \times (0, \infty ))\right)$, where each $\Omega ^{\alpha } \times (0, \infty )$ has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines $(M, {\bf g})$ up to an isometry.
LA - eng
KW - inverse scattering problem; Riemannian manifolds with cylindrical ends; waveguides
UR - http://eudml.org/doc/11231
ER -

References

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