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Linear Operators and Approximation / Lineare Operatoren und Approximation

Proceedings of the Conference held at the Oberwolfach Mathematical Research Institute, Black Forest, August 14–22, 1971 / Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach, Schwarzwald, vom 14. bis 22. August 1971

  • Conference proceedings
  • © 1972

Overview

Editors:
  1. P. L. Butzer

    1. Aachen, Germany

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  2. J.-P. Kahane

    1. Paris, France

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  3. B. Szökefalvi-Nagy

    1. Szeged, Hungary

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 20)

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Table of contents (42 papers)

  1. Front Matter

    Pages 1-17
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  2. Operator Theory

    1. Front Matter

      Pages 19-19
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    2. Generalizations of Landau’s Inequality to Linear Operators

      • Einar Hille
      Pages 20-32

    3. Semi-Groups of Nonlinear Transformations

      • J. R. Dorroh
      Pages 33-53

    4. Singular Perturbations of Semi-Group Generators

      • Irving Segal
      Pages 54-61

    5. Cyclic Vectors and Commutants

      • Béla Sz.-Nagy
      Pages 62-67

    6. Some Applications of Operator Valued Analytic Functions of Two Complex Variables

      • Joel D. Pincus
      Pages 68-79

    7. Weyl’s Theorems

      • Karl Gustafson
      Pages 80-93

    8. Some Approximation Problems in the Theory of Stationary Processes

      • Yu. A. Rozanov
      Pages 94-101

    9. Ein Operatorenkalkül für das approximationstheoretische Verhalten des Ergodensatzes im Mittel

      • P. L. Butzer, U. Westphal
      Pages 102-114

    10. A Note on the Landau—Kallman—Rota—Hille Inequality

      • W. Trebels, U. Westphal
      Pages 115-119

  3. Topics in Functional Analysis

    1. Front Matter

      Pages 121-121
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    2. Representation Theorems for Riesz Spaces

      • A. C. Zaanen
      Pages 122-128

    3. Boundedness from Measure Theory

      • Henry Helson
      Pages 129-137

    4. Exchange of Infinite Summation with Limits in Banach Spaces

      • Gerhard Grimeisen
      Pages 138-141

    5. Finite Parts of Distributions

      • J. Horváth
      Pages 142-158

    6. Courants et courants cylindriques sur des variétés de dimension infinie

      • Paul Krée
      Pages 159-174

    7. Subdefinite Functions

      • J. L. B. Cooper
      Pages 175-177

    8. Eine Bemerkung zum Banachschen Fixpunktsatz

      • Paul Otto Runck
      Pages 178-181

    9. On a Certain Converse of Hölder’s Inequality

      • L. Leindler
      Pages 182-184
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Keywords

About this book

These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In­ stitute, August 14-22, 1971. There were thirty-eight such lectures while four addi­ tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and non­ linear semi-groups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximation-theoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G.

Editors and Affiliations

  • Aachen, Germany

    P. L. Butzer

  • Paris, France

    J.-P. Kahane

  • Szeged, Hungary

    B. Szökefalvi-Nagy

Bibliographic Information

  • Book Title: Linear Operators and Approximation / Lineare Operatoren und Approximation

  • Book Subtitle: Proceedings of the Conference held at the Oberwolfach Mathematical Research Institute, Black Forest, August 14–22, 1971 / Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach, Schwarzwald, vom 14. bis 22. August 1971

  • Editors: P. L. Butzer, J.-P. Kahane, B. Szökefalvi-Nagy

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7283-6

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1972

  • Hardcover ISBN: 978-3-7643-0590-1Due: 01 January 1973

  • Softcover ISBN: 978-3-0348-7285-0Published: 08 October 2012

  • eBook ISBN: 978-3-0348-7283-6Published: 06 December 2012

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: 506

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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