### Abstract

The self-adjoint elliptic boundary-value problem in a domain with cylindrical outlets to infinity is considered. The notion of an augmented scattering matrix is introduced on the basis of artificial radiation conditions. Properties of the augmented scattering matrix are studied, and the relationship with the classical scattering matrix is demonstrated. The central point is the possibility of calculating the number of linearly independent solutions of a homogeneous problem with fixed rate of decrease at infinity by analyzing the spectrum of the augmented scattering matrix. This property is applied to the problem on diffraction on a periodic boundary as an example.

Original language | English |
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Pages (from-to) | 3657--3666 |

Number of pages | 10 |

Journal | Journal of Mathematical Sciences |

Volume | 111 |

Publication status | Published - Sep 2002 |

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## Cite this

Kamotski, I. V., & Nazarov, S. A. (2002). The Augmented Scattering Matrix and Exponentially Decaying Solutions of an Elliptic Problem in a Cylindrical Domain.

*Journal of Mathematical Sciences*,*111*, 3657--3666.