p-adic Functional Analysis

Provides the latest results on p-adic Banach spaces and locally convex spaces, spaces of analytic and continuous functions & P-adic Fourier theory and harmonic analysis. Includes basics on the theory of inductive limits of locally convex spaces. Paper. DLC: P-adic.

Preface

Contributors

1. Strict Locally Convex Topologies on BC(X,K)

1

(10)

J. Aguayo

N. de Grande-de Kimpe

S. Navarro

2. Zero-Dimensional Pseudocompact and Ultraparacompact Spaces

11

(9)

J. Aguayo

N. de Grande-de Kimpe

S. Navarro

3. Isometries in Spaces of Nonarchimedean Continuous Functions

19

(10)

Jesus Araujo

4. Isometrics Between Valued Fields

29

(10)

E. Beckenstein

L. Narici

W. Schikhof

5. Closed Homomorphisms of Algebras of Analytic Elements

39

(10)

K. Boussaf

A. Escassut

6. On Some p-adic Functional Equations

49

(12)

Abdelbaki Boutabaa

7. Complete Ultrametric Hopf Algebras Which Are Free Banach Spaces

61

(10)

Bertin Diarra

8. p-adic Characters on the Restricted Power Series

81

(14)

Bertin Diarra

Alain Escassut

Marie-Claude Sarmant

9. On Some p-adic Series with Factorials

95

(12)

Branko Dragovich

10. Non-Archimedean Harmonic Analysis on Topological Semigroups, II

107

(8)

H. A. M. Dzinotyiweyi

A. C. M. van Rooij

11. Analytic Properties of Functions Represented by p-adic Integration

115

(16)

Mikihiko Endo

12. Characterial Functions

131

(12)

Alain Escassut

Labib Haddad

Marie-Claude Sarmant

13. Nonlinear Differential Equations Over the Field of the Complex p-adic Numbers

143

(10)

Alain Escassut

Andrei Khrennikov

14. On Some Non-Archimedean Closed Graph Theorems

153

(6)

Thomas E. Gilsdorf

Jerzy Kakol

15. p-adic Locally Convex Inductive Limits

159

(64)

N. de Grande-de Kimpe

J. Kakol

C. Perez-Garcia

W. H. Schikhof

16. Some Conjectures Concerning Partial Sums of Generalized Hypergeometric Series

223

(14)

L. van Hamme

17. On Non-Archimedean Weighted Spaces of Continuous Functions

237

(16)

A. K. Katsaras

A. Beloyiannis

18. An Algebra of Self-Adjoint Operators on a Non-Archimedean Orthomodular Space

253

(12)

Hans A. Keller

Herminia Ochsenius

19. Residual Spaces and Operators on Orthomodular Spaces

265

(10)

Hans A. Keller

Herminia Ochsenius

20. Additive and Multiplicative Fractional Differentiations Over the Field of p-adic Numbers

275

(6)

Anatoly N. Kochubei

21. Algebras of Abstract Analytic Elements

281

(16)

Nicolas Mainetti

22. Some Tauberian Theorems in Non-Archimedean Fields

297

(8)

P. N. Natarajan

23. Locally Convex Modules Over the Unit Disk

305

(22)

Saskia Oortwijn

Wim Schikhof

24. Uniform Approximation of Functions with Values in Topological Rings

327

(12)

Joao B. Prolla

Ann Verdoodt

25. p-adic Almost Periodicity and Representations II

339

(10)

G. Rangan

M. S. Saleemullah

26. Euclidean Models of p-adic Spaces

349

(14)

Alain Robert

27. Analytic Functions That Are p-th Roots of Rational Functions

363

(12)

Marie-Claude Sarmant

28. Approximation Lattices of p-adic Numbers

375

(8)

Stany de Smedt

29. Adelic Formulas for Gamma-and Beta-Functions in Algebraic Number Fields

383

(14)

V. S. Vladimirov

Index

397

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p-adic Functional Analysis

Summary

Table of Contents

Supplemental Materials