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Advances in the Theory of Fréchet Spaces

  • Book
  • © 1989

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Editors:
  1. T. Terzioñlu

    1. Middle East Technical University, Ankara, Turkey

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Part of the book series: Nato Science Series C: (ASIC, volume 287)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Approximation Properties of Nuclear Frechet Spaces

    • Ed Dubinsky
    Pages 1-10

  3. Topics on Projective Spectra of (LB)-Spaces

    • Dietmar Vogt
    Pages 11-27

  4. Applications of the Projective Limit Functor to Convolution and Partial Differential Equations

    • Rüdiger W. Braun, Reinhold Meise, Dietmar Vogt
    Pages 29-46

  5. Partial Differential Operators with Continuous Linear Right Inverse

    • R. Meise, B. A. Taylor, D. Vogt
    Pages 47-62

  6. Hartogs Type Extension Theorem of Real Analytic Solutions of Linear Partial Differential Equations with Constant Coefficients

    • A. Kaneko
    Pages 63-72

  7. Remarks on the Existence of Solutions of Partial Differential Equations in Gevrey Spaces

    • L. Cattabriga
    Pages 73-78

  8. Tame Right Inverses for Partial Differential Equations

    • M. Langenbruch
    Pages 79-114

  9. Stein Spaces M for which O(M) is Isomorphic to a Power Series Space

    • Aydin Aytuna
    Pages 115-154

  10. Monomial Expansions in Infinite Dimensional Holomorphy

    • Seán Dineen
    Pages 155-171

  11. Relations between τ0 and τω on Spaces of Holomorphic Functions

    • J. M. Ansemil
    Pages 173-180

  12. Some Recent Results on VC(X)

    • Klaus D. Bierstedt, José Bonet
    Pages 181-194

  13. Projective Descriptions of Weighted Inductive Limits: The Vector-Valued Cases

    • Klaus D. Bierstedt, José Bonet
    Pages 195-221

  14. On Tensor Product α-Algebra Bundles

    • Athanasios Kyriazis
    Pages 223-233

  15. Quojection and Prequojections

    • G. Metafune, V. B. Moscatelli
    Pages 235-254

  16. Nuclear Köthe Quotients of Frechet Spaces

    • S. Önal
    Pages 255-258

  17. A Note on Strict LF-Spaces

    • José Bonet, Susanne Dierolf
    Pages 259-264

  18. Automatic Continuity in Frechet Algebras

    • M. Fragoulopoulou
    Pages 265-268

  19. Some Special Köthe Spaces

    • M. Kocatepe, Z. Nurlu
    Pages 269-296

  20. On Pelczynski’s Problem

    • J. Krone
    Pages 297-304
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Keywords

About this book

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.

Editors and Affiliations

  • Middle East Technical University, Ankara, Turkey

    T. Terzioñlu

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