# Advances in Non-Archimedean Analysis

Share this page *Edited by *
*Jesus Araujo-Gomez; Bertin Diarra; Alain Escassut*

This volume contains papers based on lectures
given at the Eleventh International Conference on \(p\)-adic
Functional Analysis, which was held from July 5–9, 2010, in
Clermont-Ferrand, France.

The articles collected here feature recent developments in various areas
of non-Archimedean analysis: Hilbert and Banach spaces, finite
dimensional spaces, topological vector spaces and operator theory,
strict topologies, spaces of continuous functions and of strictly
differentiable functions, isomorphisms between Banach function spaces,
and measure and integration.

Other topics discussed in this volume include \(p\)-adic
differential and \(q\)-difference equations, rational and
non-Archimedean analytic functions, the spectrum of some algebras of
analytic functions, and maximal ideals of the ultrametric corona
algebra.

# Table of Contents

## Advances in Non-Archimedean Analysis

- Contents vii8 free
- Preface ix10 free
- Remembering Nicole De Grande-De Kimpe (1936-2008) 112 free
- Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure 3344
- q-difference equations in ultrametric fields 3950
- Primitives of p-adic meromorphic functions 5162
- Existence of GCD's and factorization in rings of non-Archimedean entire functions 5768
- The radius of convergence function for first order differential equations 7182
- The Lipschitz condition for rational functions on ultrametric valued fields 91102
- Differential and maximal ideals of the ultrametric Corona algebra 105116
- Linear topologies on non-Archimedean function spaces 117128
- On maximal closed ideals in topological algebras of continuous vector-valued functions over non-Archimedean valued fields 135146
- Perturbations of bounded linear operators on orthomodular Hilbertian spaces 143154
- On some geometrical properties of linear subspaces of l∞ 157168
- The geometry of p-adic fractal strings: A comparative survey 163174
- Identities and congruences for Genocchi numbers 207218
- Toward an ultrametric calculus in a field K with an infinite rank valuation 221232
- Extending the multiplication of a totally ordered group to its completion 231242
- Norm Hilbert spaces with uncountable orthogonal basis 243254
- Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field 257268
- Some p-adic q-difference equations on C(Zp,K) 269280