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Advances in the Theory of Fréchet Spaces

  • T. Terzioñlu
Book

Part of the NATO ASI Series book series (ASIC, volume 287)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. R. Meise, B. A. Taylor, D. Vogt
    Pages 47-62
  3. Klaus D. Bierstedt, José Bonet
    Pages 181-194
  4. Athanasios Kyriazis
    Pages 223-233
  5. G. Metafune, V. B. Moscatelli
    Pages 235-254
  6. José Bonet, Susanne Dierolf
    Pages 259-264
  7. M. Fragoulopoulou
    Pages 265-268
  8. M. Kocatepe, Z. Nurlu
    Pages 269-296
  9. J. Krone
    Pages 297-304
  10. A. Aytuna, J. Krone, T. Terzioğlu
    Pages 325-332
  11. J. Bonet, G. Metafune, M. Maestre, V. B. Moscatelli, D. Vogt
    Pages 355-356
  12. Hikosaburo Komatsu
    Pages 357-363

About this book

Introduction

Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.

Keywords

Complex analysis convolution differential equation differential operator locally convex space partial differential equation

Editors and affiliations

  • T. Terzioñlu
    • 1
  1. 1.Middle East Technical UniversityAnkaraTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-2456-7
  • Copyright Information Springer Science+Business Media B.V. 1989
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-7608-1
  • Online ISBN 978-94-009-2456-7
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site