Inner and characteristic functions in polydiscs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910810037551104 |
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| author | Debnath, Ramlal Pradhan, Deepak K. Sarkar, Jaydeb |
| author_facet | Debnath, Ramlal Pradhan, Deepak K. Sarkar, Jaydeb |
| contents | Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inner and characteristic functions in polydiscs Debnath, Ramlal Pradhan, Deepak K. Sarkar, Jaydeb Functional Analysis Complex Variables Operator Algebras 46J15, 47A15, 30H05, 47A56, 32A35, 30J05 Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs. |
| title | Inner and characteristic functions in polydiscs |
| topic | Functional Analysis Complex Variables Operator Algebras 46J15, 47A15, 30H05, 47A56, 32A35, 30J05 |
| url | https://arxiv.org/abs/2502.00727 |