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Ultrametric Functional Analysis
Edited by: W. H. Schikhof, University of Nijmegen, The Netherlands, C. Perez-Garcia, Universidad de Cantabria, Santander, Spain, and A. Escassut, Université Blaise Pascal, Aubiére, France

Contemporary Mathematics
2003; 422 pp; softcover
Volume: 319
ISBN-10: 0-8218-3320-0
ISBN-13: 978-0-8218-3320-9
List Price: US$109
Member Price: US$87.20
Order Code: CONM/319
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This volume contains research articles based on lectures given at the Seventh International Conference on \(p\)-adic Functional Analysis.

The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, \(p\)-adic dynamical systems, and non-Archimedean probability theory and stochastic processes.

The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of \(p\)-adic groups.


Graduate students and research mathematicians interested in functional analysis, algebra, number theory, topology, theoretical physics and related areas.

Table of Contents

  • J. Aguayo and M. Nova -- Non-archimedean integral operators on the space of continuous functions
  • J. Araujo -- Isomorphisms with small bound between spaces of \(p\)-adic continuous functions
  • E. Beckenstein and L. Narici -- Automatic continuity of basis separating maps
  • M. Berz -- Cauchy theory on Levi-Civita fields
  • A. Boutabaa and A. Escassut -- Uniqueness problems and applications of the ultrametric Nevanlinna theory
  • B. Diarra -- The Hopf algebra structure of the space of continuous functions on power series over \(\mathbb{F}_q\) and Carlitz polynomials
  • N. De Grande-de Kimpe, J. Kąkol, and C. Perez-Garcia -- Metrizability of compactoid sets in non-archimedean Hausdorff (LM)-spaces
  • A. K. Katsaras -- Strict topologies and vector-measures on non-archimedean spaces
  • A. K. Katsaras and C. G. Petalas -- P-adic spaces with strict topologies as topological algebras
  • A. Khrennikov and S. Ludkovsky -- Non-archimedean stochastic processes
  • A. Khrennikov, M. Nilsson, and R. Nyqvist -- The asymptotic number of periodic points of discrete polynomial \(p\)-adic dynamical systems
  • A. N. Kochubei -- Analysis and probability over infinite extensions of a local field, II: A multiplicative theory
  • A. Kubzdela -- The Hahn-Banach subspaces of Banach spaces with base
  • A. J. Lemin and V. Lemin -- On metrically universal ultrametric spaces \(LV_{\tau}\) and \(LW_{\tau}\)
  • N. Maïnetti -- Gelfand transform and spectral radius formulae for ultrametric Banach algebras
  • P. N. Natarajan -- A theorem on summability factors for regular methods in complete ultrametric fields
  • H. Ochsenius -- Hilbert-like spaces over Krull valued fields
  • H. Ochsenius and W. H. Schikhof -- Compact operators on non-classical Hilbert spaces
  • C. Perez-Garcia -- Locally convex spaces over non-archimedean valued fields
  • C. Perez-Garcia and W. H. Schikhof -- Finite-dimensional orthocomplemented subspaces in \(p\)-adic normed spaces
  • S. Priess-Crampe and P. Ribenboim -- Systems of differential equations over valued fields
  • J. Rivera-Letelier -- Bi-analytic elements and partial isometries of hyperbolic space
  • M.-C. Sarmant -- Analytic roots of solutions of \(p\)-adic differential equations
  • K. Shamseddine and M. Berz -- Measure theory and integration on the Levi-Civita field
  • W. Śliwa -- On block basic sequences in non-archimedean Fréchet spaces
  • P.-A. Svensson -- Dynamical systems in unramified or totally ramified extensions of the \(p\)-adic number field
  • L. van Hamme -- \(p\)-adic analysis and the calculus of finite differences
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