# Advances in Ultrametric Analysis: 12th International Conference on P-adic Functional Analysis, July 2-6, 2012, University of Manitoba, Winnipeg, Manitoba, Canada

Khodr Shamseddine
American Mathematical Soc., 2013 - Mathematics - 291 pages
This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012.

The articles included in this book feature recent developments in various areas of non-archimedean analysis: branched values and zeros of the derivative of a $p$-adic meromorphic function, p-adic meromorphic functions $f^{\prime}P^{\prime}(f), g^{\prime}P^{\prime}(g)$ sharing a small function, properties of composition of analytic functions, partial fractional differentiability, morphisms between ultrametric Banach algebras of continuous functions and maximal ideals of finite dimension, the $p$-adic $q$-distributions, Banach spaces over fields with an infinite rank valuation, Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on $p$-adic spaces of continuous functions, non-Archimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in non-Archimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the Levi-Civita fileds.

Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Affine Invariant Measures in LeviCivita Vector Spaces and the Erdös Obtuse Angle Theorem 1 Some old and new results on zeros of the derivative of a adic meromorphic function 23 Survey on adic meromorphic functions sharing a small function and additional properties 31 The adic distributions 45 Morphisms between ultrametric Banach algebras and maximal ideals of finite codimension 63 Survey on branched values and exceptional values for adic meromorphic functions 73 GrobmanHartman Theorems for Diffeomorphisms of Banach Spaces over Valued Fields 79 Integral Representations of Continuous Linear Maps On adic Spaces of Continuous Functions 103
 Partial Fractional Differentiability 179 Part 1 A review on fractional differentiability in one Variable 181 Part 2 Orthogonal Bases 185 Part 3 Partial fractional differentiability in several variables 197 A Generalized Keller space over a field with a valuation of rank 205 A comprehensive survey of nonarchimedean analysis in Banach spaces over fields with an infinite rank valuation 215 All proper multiplications on the completion of a totally ordered abelian group 237 The Grothendieck approximation theory in nonArchimedean Functional Analysis 243

 Subfields of valued complete fields 123 On some classes of nonArchimedean operator algebras 133 Some identities and congruences for Stirling numbers of the second kind 149 Nonmeasurable sets in the LeviCivita field 163
 A brief survey of the study of power series and analytic functions on the LeviCivita fields 269 On nonArchimedean generalized power series spaces 281 Copyright