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

Front Cover
Khodr Shamseddine
American Mathematical Soc., 2013 - Mathematics - 291 pages
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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 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 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 non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
  

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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
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