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Abstract Spaces and Approximation / Abstrakte Räume und Approximation

Proceedings of the Conference held at the Mathematical Research Institute at Oberwolfach, Black Forest, July 18–27, 1968 / Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach, Schwarzwald, vom 18. bis 27. Juli 1968

  • Conference proceedings
  • © 1969

Overview

Editors:
  1. P. L. Butzer
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  2. B. Szőkefalvi-Nagy
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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 10)

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Table of contents (41 papers)

  1. Front Matter

    Pages 1-17
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  2. Jean Favard 1902–1965

    1. Jean Favard 1902–1965

      • G. Alexits, M. Zamansky
      Pages 19-24

  3. Operator Theory

    1. Front Matter

      Pages 25-25
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    2. Invariant Subspaces

      • P. R. Halmos
      Pages 26-30

    3. The Asymptotic Behavior of Finite Section Wiener-Hopf Equations

      • I. I. Hirschman Jr.
      Pages 31-52

    4. On the Spectrum of Toeplitz and Wiener—Hopf Operators

      • R. G. Douglas
      Pages 53-66

    5. Scattering Theory for Hyperbolic Equations

      • R. S. Phillips
      Pages 67-71

    6. Hilbertraum-Operatoren der Klasse C 0

      • Béla Sz.-Nagy
      Pages 72-81

    7. Über Potenzen von Erzeugern von Halbgruppenoperatoren

      • U. Westphal
      Pages 82-91

  4. Interpolation and Approximation on Banach Spaces

    1. Front Matter

      Pages 93-93
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    2. Interpolation Theorems for Spaces Λ

      • G. G. Lorentz, T. Shimogaki
      Pages 94-98

    3. Adjoint Operators and Interpolation of Linear Operators

      • Richard O’neil
      Pages 99-106

    4. Über Approximationsprozesse auf Banachräumen

      • Hubert Berens
      Pages 107-112

    5. Über die Fundamentalsätze der klassischen Approximationstheorie in abstrakten Räumen

      • P. L. Butzer, K. Scherer
      Pages 113-125

    6. Über die Charakterisierung von Funktionenklassen durch beste lineare Approximation

      • G. Alexits
      Pages 126-129

    7. Some Remarks and Problems on Bases in Banach Spaces

      • Ivan Singer
      Pages 130-139

    8. Nichtlineare Approximation in normierten Vektorräumen

      • Bruno Brosowski
      Pages 140-159

  5. Harmonic Analysis and Approximation

    1. Front Matter

      Pages 161-161
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    2. An Explicit Form for the Fourier-Plancherel Transform over Locally Compact Abelian Groups

      • P. Masani
      Pages 162-182

    3. Conjugacy of Transformation Groups

      • R. A. Hirschfeld
      Pages 183-189
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Keywords

About this book

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily arbitrary to some extent. The Proceedings are dedicated to the memory of Jean Favard. It was Favard who gave the Oberwolfach Conference of 1963 a special impetus and whose absence was deeply regretted this time. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa­ tures of both Alexits and Marc Zamansky. Our particular thanks are due to E.

Bibliographic Information

  • Book Title: Abstract Spaces and Approximation / Abstrakte Räume und Approximation

  • Book Subtitle: Proceedings of the Conference held at the Mathematical Research Institute at Oberwolfach, Black Forest, July 18–27, 1968 / Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach, Schwarzwald, vom 18. bis 27. Juli 1968

  • Editors: P. L. Butzer, B. Szőkefalvi-Nagy

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-5869-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1969

  • Softcover ISBN: 978-3-0348-5871-7Published: 11 April 2014

  • eBook ISBN: 978-3-0348-5869-4Published: 21 November 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: 423

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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