Entire Isometric Operators in de Branges–Pontryagin Spaces and Truncated Trigonometric Moment Problem

We develop two functional models for closed isometric entire operators V with finite deficiency indices (p, p) acting in a separable Pontryagin space K. In the first functional model it is shown that every such operator V is unitarily equivalent to a restriction TE of the backward shift operator in...

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Bibliographic Details
Published in:Complex analysis and operator theory Vol. 19; no. 5; p. 108
Main Authors: Derkach, Volodymyr, Dym, Harry
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.07.2025
Subjects:
Eigenvalues
Entire functions
Functionals
Operators
ISSN:1661-8254, 1661-8262
Online Access:Get full text
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Summary:We develop two functional models for closed isometric entire operators V with finite deficiency indices (p, p) acting in a separable Pontryagin space K. In the first functional model it is shown that every such operator V is unitarily equivalent to a restriction TE of the backward shift operator in the de Branges-Pontryagin space B(E) of p×1 vector valued entire functions. The second functional model is used to parametrize a class of compressed coresolvents of extensions V~ of V in terms of the range of a linear fractional transformation that is associated with the model. These results are applied to obtain a description of the set of solutions of an indefinite truncated trigonometric moment problem.
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ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-025-01729-z