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Product Code:  CONM/596 
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Softcover ISBN:  9780821891421 
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Book DetailsContemporary MathematicsVolume: 596; 2013; 291 ppMSC: Primary 46; 30; 12; 32; 26; 11; 47; 06
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 nonarchimedean 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, GrobmanHartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on \(p\)adic spaces of continuous functions, nonArchimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in nonArchimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the LeviCivita fields.
Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in nonarchimedean analysis as well as a broad knowledge of some of the subareas of this exciting and fastdeveloping research area.
ReadershipGraduate students and researchers interested in nonarchimedean analysis and related topics.

Table of Contents

Articles

Martin Berz and Sebastian Troncoso — Affine Invariant Measures in LeviCivita Vector Spaces and the Erdös Obtuse Angle Theorem

JeanPaul Bézivin, Kamal Boussaf and Alain Escassut — Some old and new results on zeros of the derivative of a $p$adic meromorphic function

Kamal Boussaf, Alain Escassut and Jacqueline Ojeda — Survey on $p$adic meromorphic functions $f’P’(f),\ g’P’(g)$ sharing a small function and additional properties

Bertin Diarra — The $p$adic $q$distributions

Alain Escassut and Nicolas Maïnetti — Morphisms between ultrametric Banach algebras and maximal ideals of finite codimension

Alain Escassut and Jacqueline Ojeda — Survey on branched values and exceptional values for $p$adic meromorphic functions

Helge Glöckner — GrobmanHartman Theorems for Diffeomorphisms of Banach Spaces over Valued Fields

Athanasios K. Katsaras — Integral Representations of Continuous Linear Maps On $p$adic Spaces of Continuous Functions

Hans A. Keller — Subfields of valued, complete fields

Anatoly N. Kochubei — On some classes of nonArchimedean operator algebras

Hamadoun Maïga and Fana Tangara — Some identities and congruences for Stirling numbers of the second kind

Héctor M. Moreno — Nonmeasurable sets in the LeviCivita field

Enno Nagel — Partial Fractional Differentiability

Herminia Ochsenius and Elena Olivos — A Generalized Keller space over a field with a valuation of rank $\alpha >\omega $

Herminia Ochsenius and Elena Olivos — A comprehensive survey of nonarchimedean analysis in Banach spaces over fields with an infinite rank valuation

Elena Olivos and Wim H. Schikhof — All proper multiplications on the completion of a totally ordered abelian group

Cristina PerezGarcia — The Grothendieck approximation theory in nonArchimedean Functional Analysis

Khodr Shamseddine — A brief survey of the study of power series and analytic functions on the LeviCivita fields

Wiesław Śliwa — On nonArchimedean generalized power series spaces


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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 nonarchimedean 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, GrobmanHartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on \(p\)adic spaces of continuous functions, nonArchimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in nonArchimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the LeviCivita fields.
Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in nonarchimedean analysis as well as a broad knowledge of some of the subareas of this exciting and fastdeveloping research area.
Graduate students and researchers interested in nonarchimedean analysis and related topics.

Articles

Martin Berz and Sebastian Troncoso — Affine Invariant Measures in LeviCivita Vector Spaces and the Erdös Obtuse Angle Theorem

JeanPaul Bézivin, Kamal Boussaf and Alain Escassut — Some old and new results on zeros of the derivative of a $p$adic meromorphic function

Kamal Boussaf, Alain Escassut and Jacqueline Ojeda — Survey on $p$adic meromorphic functions $f’P’(f),\ g’P’(g)$ sharing a small function and additional properties

Bertin Diarra — The $p$adic $q$distributions

Alain Escassut and Nicolas Maïnetti — Morphisms between ultrametric Banach algebras and maximal ideals of finite codimension

Alain Escassut and Jacqueline Ojeda — Survey on branched values and exceptional values for $p$adic meromorphic functions

Helge Glöckner — GrobmanHartman Theorems for Diffeomorphisms of Banach Spaces over Valued Fields

Athanasios K. Katsaras — Integral Representations of Continuous Linear Maps On $p$adic Spaces of Continuous Functions

Hans A. Keller — Subfields of valued, complete fields

Anatoly N. Kochubei — On some classes of nonArchimedean operator algebras

Hamadoun Maïga and Fana Tangara — Some identities and congruences for Stirling numbers of the second kind

Héctor M. Moreno — Nonmeasurable sets in the LeviCivita field

Enno Nagel — Partial Fractional Differentiability

Herminia Ochsenius and Elena Olivos — A Generalized Keller space over a field with a valuation of rank $\alpha >\omega $

Herminia Ochsenius and Elena Olivos — A comprehensive survey of nonarchimedean analysis in Banach spaces over fields with an infinite rank valuation

Elena Olivos and Wim H. Schikhof — All proper multiplications on the completion of a totally ordered abelian group

Cristina PerezGarcia — The Grothendieck approximation theory in nonArchimedean Functional Analysis

Khodr Shamseddine — A brief survey of the study of power series and analytic functions on the LeviCivita fields

Wiesław Śliwa — On nonArchimedean generalized power series spaces