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Ultrametric Functional Analysis
Edited by: B. Diarra and A. Escassut, Université Blaise Pascal, Aubiére, France, A. K. Katsaras, University of Ioannina, Greece, and L. Narici, St. John's University, Jamaica, NY

Contemporary Mathematics
2005; 369 pp; softcover
Volume: 384
ISBN-10: 0-8218-3684-6
ISBN-13: 978-0-8218-3684-2
List Price: US$109
Member Price: US$87.20
Order Code: CONM/384
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With contributions by leading mathematicians, this proceedings volume reflects the program of the Eighth International Conference on \(p\)-adic Functional Analysis held at Blaise Pascal University (Clermont-Ferrand, France).

Articles in the book offer a comprehensive overview of research in the area. A wide range of topics are covered, including basic ultrametric functional analysis, topological vector spaces, measure and integration, Choquet theory, Banach and topological algebras, analytic functions (in particular, in connection with algebraic geometry), roots of rational functions and Frobenius structure in \(p\)-adic differential equations, and \(q\)-ultrametric calculus.

The material is suitable for graduate students and researchers interested in number theory, functional analysis, and algebra.


Graduate students and research mathematicians interested in number theory, functional analysis, and algebra.

Table of Contents

  • J. Aguayo -- Vector measures and integral operators in the nonarchimedean setting
  • J. Aguayo, A. K. Katsaras, and S. Navarro -- On the dual space for the strict topology \(\beta_1\) and the space \(M(X)\) in function space
  • J. Aguayo, J. Goméz, M. Saavedra, and M. Wallace -- Perturbation of a \(p\)-adic dynamical system in two variables
  • J. Araujo -- Isomorphisms with small bound between spaces of \(p\)-adic continuous functions II
  • B. Diarra -- Ultrametric \(q\)-calculus
  • N. De Grande-De Kimpe and C. Perez-Garcia -- Strictness and closedness in \(p\)-adic inductive limits
  • P.-C. Hu and C.-C. Yang -- A note on Browkin-Brzeziński conjecture
  • A. K. Katsaras -- Non-Archimedean integration and strict topologies
  • H. A. Keller and H. O. A. -- Non-Archimedean orthomodular spaces and their residual spaces
  • A. N. Kochubei -- Polylogarithms and a zeta function for finite places of a function field
  • A. Kubzdela -- On finite-dimensional normed spaces over \(C_p\)
  • L. Narici and E. Beckenstein -- A non-Archimedean inner product
  • H. Ochsenius and W. H. Schikhof -- Lipschitz operators on Banach spaces over Krull valued fields
  • S. Priess-Crampe -- Remarks on some theorems of functional analysis
  • A. Pulita -- Frobenius structure for rank one \(p\)-adic differential equations
  • A. Salinier -- The ultrametric spectrum as an ordered set
  • M.-C. Sarmant -- Analytic roots of rational functions whose poles are on the unit circle
  • W. H. Schikhof -- \(p\)-adic Choquet theory
  • E. Schörner -- The spherical completion of normed vector spaces over fields with valuations of arbitrary rank
  • W. Śliwa -- On Köthe quotients of non-Archimedean Fréchet spaces
  • T. T. H. An and J. T.-Y. Wang -- Unique range sets for non-Archimedean entire functions in positive characteristic fields
  • F. Tangara -- Some continuous linear operators and orthogonal \(q\)-bases on the space of \(p\)-adic continuous functions defined on \(\mathbb{Z}_p\)
  • J. T.-Y. Wang -- Uniqueness polynomials, unique range sets and other uniqueness theorems
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