Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers, and then defines the notion of bicomplex modules. After introducing a number of no
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Daniel Alpay Maria Elena Luna-Elizarrarás Michael Shapiro Daniele C. Struppa
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
SpringerBriefs in Mathematics
Series editors Krishnaswami Alladi, Gainesville, USA Nicola Bellomo, Torino, Italy Michele Benzi, Atlanta, USA Tatsien Li, Shanghai, People’s Republic of China Matthias Neufang, Ottawa, Canada Otmar Scherzer, Vienna, Austria Dierk Schleicher, Bremen, Germany Vladas Sidoravicius, Rio de Janeiro, Brazil Benjamin Steinberg, New York, USA Yuri Tschinkel, New York, USA Loring W. Tu, Medford, USA G. George Yin, Detroit, USA Ping Zhang, Kalamazoo, USA
SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians. For further volumes: http://www.springer.com/series/10030
Daniel Alpay Maria Elena Luna-Elizarrarás Michael Shapiro Daniele C. Struppa •
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Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
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Daniel Alpay Department of Mathematics Ben-Gurion University of the Negev Beer Sheva Israel
Daniele C. Struppa Schmid College of Science and Technology Chapman University Orange, CA USA
Maria Elena Luna-Elizarrarás Michael Shapiro Departamento de Matemáticas ESFM-IPN Mexico, DF Mexico
ISSN 2191-8198 ISSN 2191-8201 (electronic) ISBN 978-3-319-05109-3 ISBN 978-3-319-05110-9 (eBook) DOI 10.1007/978-3-319-05110-9 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014932535 The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that s
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