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.

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)

References in corpus (3)

• The inverse scattering problem for metric graphs and the traveling salesman problem
• Time-Dispersive Behaviour as a Feature of Critical Contrast Media
• The functional model for maximal dissipative operators: An approach in the spirit of operator knots

Cited by in corpus (2)

• Functional model for boundary-value problems
• Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions