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April 2019 On the Lax–Phillips scattering matrix of the abstract wave equation
M. Gawlik, A. Główczyk, S. Kuzhel
Banach J. Math. Anal. 13(2): 449-467 (April 2019). DOI: 10.1215/17358787-2018-0048

Abstract

We study the dependence of singularities of scattering matrices of the abstract wave equation on the choice of asymptotically equivalent outgoing/incoming subspaces. We apply the obtained results to the radial wave equation with nonlocal potential. In the latter case, the concept of associated inner function—introduced by Douglas, Shapiro, and Shields in 1970—plays an essential role.

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M. Gawlik. A. Główczyk. S. Kuzhel. "On the Lax–Phillips scattering matrix of the abstract wave equation." Banach J. Math. Anal. 13 (2) 449 - 467, April 2019. https://doi.org/10.1215/17358787-2018-0048

Information

Received: 22 August 2018; Accepted: 9 December 2018; Published: April 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07045467
MathSciNet: MR3927882
Digital Object Identifier: 10.1215/17358787-2018-0048

Subjects:
Primary: 47B25
Secondary: 35P05

Keywords: inner function , Lax–Phillips scattering approach , noncyclic function , scattering matrix , simple maximal symmetric operator

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 2 • April 2019
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