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Published in:
2020 | OriginalPaper | Chapter
Scattering theory for a class of non-selfadjoint extensions of symmetric operators
Authors : Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
Published in: Analysis as a Tool in Mathematical Physics
Publisher: Springer International Publishing
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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.