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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 selfadjoint and nonselfadjoint situations.
Original language  English 

Title of host publication  Operator Theory 
Subtitle of host publication  Advances and Applications 
Editors  P. Kurasov, A. Laptev , S. Naboko, B. Simon 
Place of Publication  Cham, Switzerland 
Publisher  Springer 
Pages  194230 
Number of pages  37 
ISBN (Electronic)  9783030315313 
ISBN (Print)  9783030315306 
DOIs  
Publication status  Epub ahead of print  15 Jul 2020 
Publication series
Name  Operator Theory: Advances and Applications 

Volume  276 
ISSN (Print)  02550156 
ISSN (Electronic)  22964878 
Keywords
 Boundary triples
 Extensions of symmetric operators
 Functional model
 Scattering theory
ASJC Scopus subject areas
 Analysis
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From functional models of operator theory to materials science: new vistas through BathUNAM partnership
Cherednichenko, K., Spence, E., Silva, L. O., Ballesteros, M. & Kiselev, A.
1/01/20 → 31/12/21
Project: Researchrelated funding

BathChileMexico Network
Kyprianou, A., Majumdar, A., Cherednichenko, K., Cox, A., Musso, M., Del Pino, M., Majumdar, A., Maas, A., Jara, A., Rivero, V. & Benítez, H.
1/07/18 → 31/08/20
Project: Researchrelated funding

Newton Mobility Grant : Homogenisation of Degenerate Equations and Scattering for New Materials
1/02/17 → 31/01/19
Project: Research council