Ultrametric Functional Analysis

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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.

Read More Show Less

Product Details

  • ISBN-13: 9780821833209
  • Publisher: American Mathematical Society
  • Publication date: 3/24/2003
  • Series: Contemporary Mathematics Series , #319
  • Pages: 422
  • Product dimensions: 72.50 (w) x 10.00 (h) x 1.00 (d)

Table of Contents

Preface
Non-archimedean integral operators on the space of continuous functions 1
Isomorphisms with small bound between spaces of p-adic continuous functions 17
Automatic continuity of basis separating maps 29
Cauchy theory on Levi-Civita fields 39
Uniqueness problems and applications of the ultrametric Nevanlinna theory 53
The Hopf algebra structure of the space of continuous functions on power series over F[subscript q] and Carlitz polynomials 75
Metrizability of compactoid sets in non-archimedean Hausdorff (LM)-spaces 99
Strict topologies and vector-measures on non-archimedean spaces 109
p-adic spaces with strict topologies as topological algebras 131
Non-archimedean stochastic processes 139
The asymptotic number of periodic points of discrete polynomial p-adic dynamical systems 159
Analysis and probability over infinite extensions of a local field. II: A multiplicative theory 167
The Hahn-Banach subspaces of Banach spaces with base 179
On metrically universal ultrametric spaces LV[subscript [tau]] and LW[subscript [tau]] 191
Gelfand transform and spectral radius formulae for ultrametric Banach algebras 207
A theorem on summability factors for regular methods in complete ultrametric fields 223
Hilbert-like spaces over Krull valued fields 227
Compact operators on non-classical Hilbert spaces 239
Locally convex spaces over non-archimedean valued fields 251
Finite-dimensional orthocomplemented subspaces in p-adic normed spaces 281
Systems of differential equations over valued fields 299
Bi-analytic elements and partial isometries of hyperbolic space 319
Analytic roots of solutions of p-adic differential equations 345
Measure theory and integration on the Levi-Civita field 369
On block basic sequences in non-archimedean Frechet spaces 389
Dynamical systems in unramified or totally ramified extensions of the p-adic number field 405
p-adic analysis and the calculus of finite differences 413
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