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Complex Analysis on Infinite Dimensional Spaces

  • Seán Dineen

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Seán Dineen
    Pages 1-81
  3. Seán Dineen
    Pages 83-141
  4. Seán Dineen
    Pages 243-322
  5. Seán Dineen
    Pages 323-396
  6. Seán Dineen
    Pages 397-445
  7. Back Matter
    Pages 447-543

About this book

Introduction

Infinite dimensional holomorphy is the study of holomorphic or analytic func­ tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself ini­ tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suit­ able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.

Keywords

Complex analysis Holomorphic Extension Nevanlinna theory calculus topology

Authors and affiliations

  • Seán Dineen
    • 1
  1. 1.Department of MathematicsUniversity College DublinBelfield Dublin 4Ireland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0869-6
  • Copyright Information Springer-Verlag London 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4471-1223-5
  • Online ISBN 978-1-4471-0869-6
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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