On the Lax-Phillips scattering matrix of the abstract wave equation. (English) Zbl 1482.47020

Summary: 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 [R. G. Douglas et al., Ann. Inst. Fourier 20, No. 1, 37–76 (1970; Zbl 0186.45302)] – plays an essential role.


47A40 Scattering theory of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35L90 Abstract hyperbolic equations


Zbl 0186.45302
Full Text: DOI arXiv Euclid


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