Functional Analysis and Approximation

1. Front Matter

   Pages 1-10

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2. Zur Tagung

   1. Zur Tagung

      • P. L. Butzer, E. Görlich, B. Sz.-Nagy

      Pages 11-11

3. List of Participants

   1. List of Participants

      • P. L. Butzer, B. Sz.-Nagy, E. Görlich

      Pages 12-14

4. Program of the Sessions

   1. Program of the Sessions

      • P. L. Butzer, B. Sz.-Nagy, E. Görlich

      Pages 15-17

5. Jacob Lionel Bakst Cooper — In Memoriam

   1. Jacob Lionel Bakst Cooper — In Memoriam

      • P. L. Butzer

      Pages 19-23

6. A Testimony from a Friend

   1. A Testimony from a Friend

      • A. J. W. Hill

      Pages 25-26

7. Operator Theory

   1. Front Matter

      Pages 27-27

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   2. Fixed Points of Certain Maps on Positive Semidefinite Operators

      • T. Ando

      Pages 29-38

   3. A Remark on the Spectral Bound of the Generator of Semigroups of Positive Operators with Applications to Stability Theory

      • Manfred Wolff

      Pages 39-50

   4. Local Operators, Regular Sets, and Evolution Equations of Diffusion Type

      • Gunter Lumer

      Pages 51-71

   5. An Outline of the Spectral Theory of Propagators

      • P. Masani

      Pages 73-84

   6. On Generalized Inverses and Operator Ranges

      • M. Z. Nashed

      Pages 85-96

8. Functional Analysis

   1. Front Matter

      Pages 97-97

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   2. Modular Approximation by a Filtered Family of Linear Operators

      • Julian Musielak

      Pages 99-110

   3. Interpolation between H1 and L∞

      • Colin Bennett, Robert Sharpley

      Pages 111-116

   4. The Franklin Orthogonal System as Unconditional Basis in ReH¹ and VMO

      • Zbigniew Ciesielski

      Pages 117-125

9. Abstract Harmonic Analysis

   1. Front Matter

      Pages 127-127

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   2. Bessel Potential Spaces and Generalized Lipschitz Spaces on Local Fields

      • H. Ombe, C. W. Onneweer

      Pages 129-137

   3. On the Minimum Norm Property of the Fourier Projection in L1-Spaces

      • P. V. Lambert

      Pages 139-152

   4. Banach Spaces of Distributions of Wiener’s Type and Interpolation

      • Hans G. Feichtinger

      Pages 153-165

These Proceedings form a record of the lectures presented at the interna­ tional Conference on Functional Analysis and Approximation held at the Ober­ wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera­ tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.

• Distribution
• Evolution
• Operator theory
• calculus
• convolution
• functional analysis
• harmonic analysis
• integral transform
• mathematics

• Lehrstuhl A für Mathematik, Rhein.-Westf. Techn. Hochschule Aachen, Aachen, Germany

  P. L. Butzer, E. Görlich

• József Attila Tudományegyetem, Szeged, Hungary

  B. Sz.-Nagy

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