Ghosh, Gargi and Hazra, Somnath (2022) On analytic structure of weighted shifts on generalized directed semi-trees. In: Linear and Multilinear Algebra . pp. 1-20. ISSN 0308-1087
Full text not available from this repository.Abstract
Inspired by natural classes of examples, we define generalized directed semi-trees and construct weighted shifts on them. Given an n-tuple of generalized directed semi-trees with certain properties, we associate an n-tuple of multiplication operators on a Hilbert space (Formula presented.) of formal power series. Under certain conditions, (Formula presented.) turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in (Formula presented.) and the n-tuple of multiplication operators on (Formula presented.) is unitarily equivalent to an n-tuple of weighted shifts on generalized directed semi-trees. Finally, we exhibit two classes of examples of n-tuples of operators, which can be intrinsically identified as weighted shifts on generalized directed semi-trees.
| Item Type: | Journal Article |
|---|---|
| Publication: | Linear and Multilinear Algebra |
| Publisher: | Taylor and Francis Ltd. |
| Additional Information: | The copyright of this article belongs to the Authors. |
| Keywords: | elementary symmetric polynomial; generalized directed semi-tree; Schur polynomial; Weighted shift |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 May 2022 05:11 |
| Last Modified: | 23 May 2022 05:11 |
| URI: | https://eprints.iisc.ac.in/id/eprint/72395 |
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