Abstract Spaces and Approximation / Abstrakte Räume und Approximation

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

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.

• addition
• approximation
• approximation theory
• banach spaces
• boundary element method
• communication
• function
• functional
• functional analysis
• interpolation
• Mathematica
• operator
• scattering theory
• theorem
• time

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