**Contemporary Mathematics**

Volume: 384;
2005;
369 pp;
Softcover

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

Print ISBN: 978-0-8218-3684-2

Product Code: CONM/384

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

**Electronic ISBN: 978-0-8218-7974-0
Product Code: CONM/384.E**

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

# Ultrametric Functional Analysis

Share this page *Edited by *
*B. Diarra; A. Escassut; A. K. Katsaras; L. Narici*

With contributions by leading mathematicians, this proceedings volume reflects the program of the Eighth International Conference on \(p\)-adic Functional Analysis held at Blaise Pascal University (Clermont-Ferrand, France).

Articles in the book offer a comprehensive overview of research in the area. A wide range of topics are covered, including basic ultrametric functional analysis, topological vector spaces, measure and integration, Choquet theory, Banach and topological algebras, analytic functions (in particular, in connection with algebraic geometry), roots of rational functions and Frobenius structure in \(p\)-adic differential equations, and \(q\)-ultrametric calculus.

The material is suitable for graduate students and researchers interested in number theory, functional analysis, and algebra.

#### Readership

Graduate students and research mathematicians interested in number theory, functional analysis, and algebra.

# Table of Contents

## Ultrametric Functional Analysis

- Contents v6 free
- Preface vii8 free
- Vector measures and integral operators in the non-Archimedean setting 110 free
- On the dual space for the strict topology β1 and the space M(X) in function space 1524
- Perturbation of a p-adic dynamical system in two variables 3948
- Isomorphisms with small bound between spaces of p-adic continuous functions II 5362
- Ultrametric q-calculus 6372
- Strictness and closedness in p-adic inductive limits 7988
- A note on Browkin-Brzeziński conjecture 101110
- Non-Archimedean integration and strict topologies 111120
- Non-Archimedean orthomodular spaces and their residual spaces 145154
- Polylogarithms and a zeta function for finite places of a function field 157166
- On finite-dimensional normed spaces over Cp 169178
- A non-Archimedean inner product 187196
- Lipschitz operators on Banach spaces over Krull valued fields 203212
- Remarks on some theorems of functional analysis 235244
- Frobenius structure for rank one p-adic differential equations 247256
- The ultrametric spectrum as an ordered set 259268
- Analytic roots of rational functions whose poles are on the unit circle 271280
- p-adic Choquet Theory 281290
- The spherical completion of normed vector spaces over fields with valuations of arbitrary rank 299308
- On Köthe quotients of non-Archimedean Fréchet spaces 309318
- Unique range sets for non-Archimedean entire functions in positive characteristic fields 323332
- Some continuous linear operators and orthogonal q-bases on the space of p-adic continuous functions defined on Zp 335344
- Uniqueness polynomials, unique range sets and other uniqueness theorems 353362