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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| Vydané v: | Complex analysis and operator theory Ročník 19; číslo 5; s. 108 |
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01.07.2025
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 108 |
| Author | Dym, Harry Derkach, Volodymyr |
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| Title | Entire Isometric Operators in de Branges–Pontryagin Spaces and Truncated Trigonometric Moment Problem |
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