Reproducing Kernel Spaces and Realizations

The tools developed in the previous chapters allow us to define and study in the operator-valued case the various families of functions appearing in classical Schur analysis. In this section we obtain realization formulas for these functions. These formul

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Daniel Alpay Fabrizio Colombo Irene Sabadini

Slice Hyperholomorphic Schur Analysis

Operator Theory: Advances and Applications Volume 256 Founded in 1979 by Israel Gohberg

Editors: Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Wien, Austria) Christiane Tretter (Bern, Switzerland) Associate Editors: Vadim Adamyan (Odessa, Ukraine) Wolfgang Arendt (Ulm, Germany) Albrecht Böttcher (Chemnitz, Germany) B. Malcolm Brown (Cardiff, UK) Raul Curto (Iowa, IA, USA) Fritz Gesztesy (Columbia, MO, USA) Pavel Kurasov (Stockholm, Sweden) Vern Paulsen (Houston, TX, USA) Mihai Putinar (Santa Barbara, CA, USA) Ilya M. Spitkovsky (Williamsburg, VA, USA)

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Subseries Linear Operators and Linear Systems Subseries editors: Daniel Alpay (Orange, CA, USA) Birgit Jacob (Wuppertal, Germany) André C.M. Ran (Amsterdam, The Netherlands) Subseries Advances in Partial Differential Equations Subseries editors: Bert-Wolfgang Schulze (Potsdam, Germany) Michael Demuth (Clausthal, Germany) Jerome A. Goldstein (Memphis, TN, USA) Nobuyuki Tose (Yokohama, Japan) Ingo Witt (Göttingen, Germany)

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Daniel Alpay • Fabrizio Colombo • Irene Sabadini

Slice Hyperholomorphic Schur Analysis

Daniel Alpay Department of Mathematics Chapman University Orange, California, USA

Fabrizio Colombo Dipartimento di Matematica Politecnico di Milano Milano, Italy

Irene Sabadini Dipartimento di Matematica Politecnico di Milano Milano, Italy

ISSN 0255-0156 ISSN 2296-4878 (electronic) Operator Theory: Advances and Applications ISBN 978-3-319-42513-9 ISBN 978-3-319-42514-6 (eBook) DOI 10.1007/978-3-319-42514-6 Library of Congress Control Number: 2016960537 Mathematics Subject Classification (2010): 30G35, 46C20, 47B32, 30E05

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