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Advances in Ultrametric Analysis
Edited by: Khodr Shamseddine, University of Manitoba, Winnipeg, Manitoba, Canada
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Contemporary Mathematics
2013; 291 pp; softcover
Volume: 596
ISBN-10: 0-8218-9142-1
ISBN-13: 978-0-8218-9142-1
List Price: US$100
Member Price: US$80
Order Code: CONM/596
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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.

Readership

Graduate students and researchers interested in non-archimedean analysis and related topics.

Table of Contents

  • M. Berz and S. Troncoso -- Affine invariant measures in Levi-Civita vector spaces and Erdös obtuse angle theorem
  • J.-P. Bézivin, K. Boussaf, and A. Escassut -- Some old and new results on zeros of the derivative of a \(p\)-adic meromorphic function
  • K. Boussaf, A. Escassut, and J. Ojeda -- Survey on \(p\)-adic meromorphic functions \(f'P'(f), g'P'(g)\) sharing a small function and additional properties
  • B. Diarra -- The \(p\)-adic \(q\)-distributions
  • A. Escassut and N. Maïnetti -- Morphisms between ultrametric Banach algebras and maximal ideals of finite codimension
  • A. Escassut and J. Ojeda -- Survey on branched values and exceptional values for \(p\)-adic meromorphic functions
  • H. Glöckner -- Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields
  • A. K. Katsaras -- Integral representations of continuous linear maps on \(p\)-adic spaces of continuous functions
  • H. A. Keller -- Subfields of valued, complete fields
  • A. N. Kochubei -- On some classes of non-Archimedean operator algebras
  • H. Maïga and F. Tangara -- Some identities and congruences for Stirling numbers of the second kind
  • H. M. Moreno -- Non-measurable sets in the Levi-Civita field
  • E. Nagel -- Partial fractional differentiability
  • H. Ochsenius and E. Olivos -- A generalized space over a field with a valuation of rank \(\alpha >\omega\)
  • H. Ochsenius and E. Olivos -- A comprehensive survey of non-archimedean analysis in Banach spaces over fields with an infinite rank valuation
  • E. Olivos and W. H. Schikhof -- All proper multiplications on the completion of a totally ordered albelian group
  • C. Perez-Garcia -- The Grothendieck approximation theory in non-archimedean functional analysis
  • K. Shamseddine -- A brief survey of the study of power series and analytic functions on the Levi-Civita fields
  • W. Śliwa -- On non-archimedean generalized power series spaces
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