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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

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.

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

• 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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