Approximation Theory and Functional Analysis

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Front Cover 2
Approximation Theory and Functional Analysis 5
Copyright Page 6
Foreword 7
Table of Contents 9
Chapter 1. Polynomial approximation and a question of G. E. Shilov 11
Chapter 2. Analytic hypoellipticity of operators of principal type 23
Chapter 3. Korovkin approximation in function spaces 29
Chapter 4. A remark on vector-valued approximation on compact sets, approximation on product sets, and the approximation propert 47
Chapter 5. The completion of partially ordered vector spaces and Korovkin’s theorem 73
Chapter 6. Approximation by algebraic convolution integrals 81
Chapter 7. Non-archimedean weighted approximation 131
Chapter 8. Thèorie spectrale en une infinite de variables 143
Chapter 9. Meromorphic uniform approximation on closed subsets of open Riemann surfaces 149
Chapter 10. Whitney’s spectral synthesis theorem in infinite dimensions 169

Front Cover 2
Approximation Theory and Functional Analysis 5
Copyright Page 6
Foreword 7
Table of Contents 9
Chapter 1. Polynomial approximation and a question of G. E. Shilov 11
Chapter 2. Analytic hypoellipticity of operators of principal type 23
Chapter 3. Korovkin approximation in function spaces 29
Chapter 4. A remark on vector-valued approximation on compact sets, approximation on product sets, and the approximation propert 47
Chapter 5. The completion of partially ordered vector spaces and Korovkin’s theorem 73
Chapter 6. Approximation by algebraic convolution integrals 81
Chapter 7. Non-archimedean weighted approximation 131
Chapter 8. Thèorie spectrale en une infinite de variables 143
Chapter 9. Meromorphic uniform approximation on closed subsets of open Riemann surfaces 149
Chapter 10. Whitney’s spectral synthesis theorem in infinite dimensions 169
Chapter 11. Recent progess in Birkhoff interpolation 197
Chapter 12. Approximation polynomiale ponderèe et produits canoniques 247
Chapter 13. Spaces of differentiable functions and the approximation property 273
Chapter 14. A look at approximation theory 319
Chapter 15. Banach algebras over valued fields 343
Chapter 16. Approximation of plurisubharmonic functions 353
Chapter 17. The approximation property for certain spaces of holomorphic mappings 361
Chapter 18. The approximation property for Nachbin spaces 381
Chapter 19. On cardinal spline smoothing 393
Chapter 20. A characterization of echelon köthe-Schwartz spaces 419
Chapter 21. The rational approximation of real functions 431
Chapter 22. Fundamental seminorms 439
Index 455

Proceedings of the International Symposium on Approximation Theory, Universidade Estadual de Campinas (UNICAMP) Brazil, August 1-5, 1977

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