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On analytic structure of weighted shifts on generalized directed semi-trees

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

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Official URL: https://doi.org/10.1080/03081087.2022.2065233

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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