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On a Polyanalytic Approach to Noncommutative de Branges–Rovnyak Spaces and Schur Analysis

Authors
  • Alpay, Daniel1
  • Colombo, Fabrizio2
  • Diki, Kamal2
  • Sabadini, Irene2
  • 1 Chapman University, One University Drive, Orange, CA, 92866, USA , Orange (United States)
  • 2 Dipartimento di Matematica, Via E. Bonardi, 9, Milan, 20133, Italy , Milan (Italy)
Type
Published Article
Journal
Integral Equations and Operator Theory
Publisher
Springer International Publishing
Publication Date
Jun 21, 2021
Volume
93
Issue
4
Identifiers
DOI: 10.1007/s00020-021-02649-1
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Green

Abstract

In this paper we begin the study of Schur analysis and of de Branges–Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, and allows us to make connections with the recently developed theory of slice polyanalytic functions. We tackle a number of problems: we describe a Hardy space, Schur multipliers and related results. We also discuss Blaschke functions, Herglotz multipliers and their associated kernels and Hilbert spaces. Finally, we consider the counterpart of the half-space case, and the corresponding Hardy space, Schur multipliers and Carathéodory multipliers.

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