**Contemporary Mathematics**

Volume: 319;
2003;
422 pp;
Softcover

MSC: Primary 11; 12; 16; 30; 37; 46; 47; 54; 60;

Print ISBN: 978-0-8218-3320-9

Product Code: CONM/319

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

**Electronic ISBN: 978-0-8218-7909-2
Product Code: CONM/319.E**

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

# Ultrametric Functional Analysis

Share this page *Edited by *
*W. H. Schikhof; C. Perez-Garcia; A. Escassut*

This volume contains research articles based on lectures given at the Seventh
International Conference on \(p\)-adic Functional Analysis.

The articles, written by leading international experts, provide a complete
overview of the latest contributions in basic functional analysis (Hilbert and
Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces
of continuous functions, strict topologies, operator theory, automatic
continuity, measure and integrations, Banach and topological algebras,
summability methods, and ultrametric spaces), analytic functions (meromorphic
functions, roots of rational functions, characterization of injective
holomorphic functions, and Gelfand transforms in algebras of analytic
functions), differential equations, Banach-Hopf algebras, Cauchy theory of
Levi-Civita fields, finite differences, weighted means, \(p\)-adic
dynamical systems, and non-Archimedean probability theory and stochastic
processes.

The book is written for graduate students and research mathematicians. It
also would make a good reference source for those in related areas, such as
classical functional analysis, complex analytic functions, probability theory,
dynamical systems, orthomodular spaces, number theory, and representations of
\(p\)-adic groups.

#### Readership

Graduate students and research mathematicians interested in functional analysis, algebra, number theory, topology, theoretical physics and related areas.

# Table of Contents

## Ultrametric Functional Analysis

- Contents vii8 free
- Preface ix10 free
- Non-archimedean integral operators on the space of continuous functions 112 free
- Isomorphisms with small bound between spaces of p-adic continuous functions 1728
- Automatic continuity of basis separating maps 2940
- Cauchy theory on Levi-Civita fields 3950
- Uniqueness problems and applications of the ultrametric Nevanlinna theory 5364
- The Hopf algebra structure of the space of continuous functions on power series over Fq and Carlitz polynomials 7586
- Metrizability of compactoid sets in non-archimedean Hausdorff (LM)-spaces 99110
- Strict topologies and vector-measures on non-archimedean spaces 109120
- p-adic spaces with strict topologies as topological algebras 131142
- Non-archimedean stochastic processes 139150
- The asymptotic number of periodic points of discrete polynomial p-adic dynamical systems 159170
- Analysis and probability over infinite extensions of a local field, II: A multiplicative theory 167178
- The Hahn-Banach subspaces of Banach spaces with base 179190
- On metrically universal ultrametric spaces LV┬ and LW┬ 191202
- Gelfand transform and spectral radius formulae for ultrametric Banach algebras 207218
- A theorem on summability factors for regular methods in complete ultrametric fields 223234
- Hilbert-like spaces over Krull valued fields 227238
- Compact operators on non-classical Hilbert spaces 239250
- Locally convex spaces over non-archimedean valued fields 251262
- Finite-dimensional orthocomplemented subspaces in p-adic normed spaces 281292
- Systems of differential equations over valued fields 299310
- Bi-analytic elements and partial isometries of hyperbolic space 319330
- 1. Introduction. 320331
- 2. Preliminaries. 322333
- 3. Hyperbolic Space. 322333
- 4. Distance δ on Cp U HP. 323334
- 5. Geometry of Cp U Hp. 326337
- 6. Partial isometries of Hp. 328339
- 7. Open affinoids and circular filters. 329340
- 8. Rational maps. 332343
- 9. Local isometries induced by rational maps. 334345
- 10. Extension of an analytic element. 336347
- 11. Composition of analytic elements and bi-analytic elements. 338349
- 12. Global properties of bi-analytic elements. 340351
- 13. Appendix: analytic elements and ends. 342353
- References 343354

- Analytic roots of solutions of p-adic differential equations 345356
- Measure theory and integration on the Levi-Civita field 369380
- On block basic sequences in non-archimedean Fréchet spaces 389400
- Dynamical systems in unramified or totally ramified extensions of the p-adic number field 405416
- p-adic analysis and the calculus of finite differences 413424