Scattering theory for a class of non-selfadjoint extensions of symmetric operators
Abstract
This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.
Keywords
Cite
@article{arxiv.1712.09293,
title = {Scattering theory for a class of non-selfadjoint extensions of symmetric operators},
author = {Kirill D. Cherednichenko and Alexander V. Kiselev and Luis O. Silva},
journal= {arXiv preprint arXiv:1712.09293},
year = {2020}
}
Comments
32 pages; This is the continuation of arXiv:1703.06220 (and formerly contained in v1); this version is as accepted by the journal (Operator Theory: Advances and Applications)