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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| Published in: | Complex analysis and operator theory Vol. 19; no. 5; p. 108 |
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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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| Cites_doi | 10.1007/978-3-0348-5483-2_5 10.1090/S0002-9947-1939-1501997-7 10.1016/j.jfa.2020.108776 10.1007/s11785-020-01073-4 10.1007/BF01086749 10.1007/BF01202812 10.1007/s00020-009-1709-7 10.1007/978-3-642-65567-8 10.1007/978-3-0348-5472-6_5 10.1002/1522-2616(200011)219:1<5::AID-MANA5>3.0.CO;2-L 10.1090/cbms/071 10.4213/mzm618 10.1016/0022-1236(78)90064-2 10.2140/pjm.1986.125.347 10.1007/978-3-0348-8908-7 10.1515/9783112735992 10.2140/pjm.1961.11.9 10.2140/pjm.1969.28.503 10.1007/s11785-024-01591-5 10.1016/j.jfa.2018.10.018 10.1007/978-3-0348-7709-1 10.1007/s00020-020-02595-4 10.1007/BF02367240 10.1007/BF02786620 10.1007/BF01075777 10.1090/S0002-9947-1950-0051437-7 10.1007/s00020-003-1236-x 10.1070/IM1984v022n03ABEH001452 10.1007/s11785-009-0031-3 10.1017/CBO9780511721427 10.1007/s00020-003-1220-5 |
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| Title | Entire Isometric Operators in de Branges–Pontryagin Spaces and Truncated Trigonometric Moment Problem |
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