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Recent Advances in Operator Theory pp 361–383Cite as

Birkhäuser

Scattering of Waves by Periodic Gratings and Factorization Problems

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 124))

Abstract

The paper deals with scattering problems of plane and space waves by periodic gratings in ℝ3 and ℝ3, respectively. The plane problem caused a vast physical and mathematical literature starting from the papers of Rayleigh. A new approach to treat this problem is proposed in the present paper. It is based on the possibility to reformulate the scattering problem in terms of abstract ordinary differential equation with constant operator coefficients on a Hilbert space. The solvability of such equations with radiation conditions at the infinity is based on the factorization of the operator symbol of the equation. This approach is general and allows, in particular, to solve the scattering problem of a space wave in ℝ3.

Dedicated to Israel Gohberg on the occasion of his 70th birthday

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow Lomonosov University, Moscow, 119899, Russia

    A. G. Kostyuchenko & A. A. Shkalikov

Authors
  1. A. G. Kostyuchenko
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  2. A. A. Shkalikov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    A. Dijksma

  2. Division of Mathematics and Computer Science Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek  & A. C. M. Ran  & 

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© 2001 Springer Basel AG

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Kostyuchenko, A.G., Shkalikov, A.A. (2001). Scattering of Waves by Periodic Gratings and Factorization Problems. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_17

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9516-3

  • Online ISBN: 978-3-0348-8323-8

  • eBook Packages: Springer Book Archive

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