$$\varvec{q}$$-rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels
Abstract In this paper we introduce the concept of matrix-valued q -rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q -deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.
Authors
- Paula Cerejeiras (ORCID: https://orcid.org/0000-0001-7667-4595)
- Daniel Alpay (ORCID: https://orcid.org/0000-0002-7612-3598)
- Uwe Käehler (ORCID: https://orcid.org/0000-0002-9066-1819)
- Baruch Schneider (ORCID: https://orcid.org/0000-0003-2933-3899)
Institutions
- Chapman University (US)
- University of Ostrava (CZ)
- University of Aveiro (PT)
Publication Details
- Journal
- Integral Equations and Operator Theory
- Published
- 2024-09-14
- DOI
- https://doi.org/10.1007/s00020-024-02779-2
- Primary Topic
- Mathematical functions and polynomials
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Center for Research and Development in Mathematics and Applications
- Fundação para a Ciência e a Tecnologia
- Division of Mathematical Sciences