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Advances in Ultrametric Analysis
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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 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.
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Table of Contents

Affine invariant measures in Levi-Civita vector spaces and Erdos obtuse angle theorem by M. Berz and S. TroncosoSome old and new results on zeros of the derivative of a $p$-adic meromorphic function by J.-P. Bezivin, K. Boussaf, and A. EscassutSurvey on $p$-adic meromorphic functions $f'P'(f), g'P'(g)$ sharing a small function and additional properties by K. Boussaf, A. Escassut, and J. OjedaThe $p$-adic $q$-distributions by B. Diarra Morphisms between ultrametric Banach algebras and maximal ideals of finite codimension by A. Escassut and N. MainettiSurvey on branched values and exceptional values for $p$-adic meromorphic functions by A. Escassut and J. OjedaGrobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields by H. GlocknerIntegral representations of continuous linear maps on $p$-adic spaces of continuous functions by A. K. KatsarasSubfields of valued, complete fields by H. A. KellerOn some classes of non-Archimedean operator algebras by A. N. KochubeiSome identities and congruences for Stirling numbers of the second kind by H. Maiga and F. TangaraNon-measurable sets in the Levi-Civita field by H. M. MorenoPartial fractional differentiability by E. NagelA generalized space over a field with a valuation of rank $alpha >omega$ by H. Ochsenius and E. OlivosA comprehensive survey of non-archimedean analysis in Banach spaces over fields with an infinite rank valuation by H. Ochsenius and E. OlivosAll proper multiplications on the completion of a totally ordered albelian group by E. Olivos and W. H. SchikhofThe Grothendieck approximation theory in non-archimedean functional analysis by C. Perez-GarciaA brief survey of the study of power series and analytic functions on the Levi-Civita fields by K. ShamseddineOn non-archimedean generalized power series spaces by W. Sliwa

About the Author

Khodr Shamseddine, University of Manitoba, Winnipeg, Manitoba, Canada

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