Ultrametric Functional Analysis.

Intro -- Contents -- Preface -- Non-archimedean integral operators on the space of continuous functions -- Isomorphisms with small bound between spaces of p-adic continuous functions -- Automatic continuity of basis separating maps -- Cauchy theory on Levi-Civita fields -- Uniqueness problems and applications of the ultrametric Nevanlinna theory -- The Hopf algebra structure of the space of continuous functions on power series over Fq and Carlitz polynomials -- Metrizability of compactoid sets in non-archimedean Hausdorff (LM)-spaces -- Strict topologies and vector-measures on non-archimedean spaces -- p-adic spaces with strict topologies as topological algebras -- Non-archimedean stochastic processes -- The asymptotic number of periodic points of discrete polynomial p-adic dynamical systems -- Analysis and probability over infinite extensions of a local field, II: A multiplicative theory -- The Hahn-Banach subspaces of Banach spaces with base -- On metrically universal ultrametric spaces LV┬ and LW┬ -- Gelfand transform and spectral radius formulae for ultrametric Banach algebras -- A theorem on summability factors for regular methods in complete ultrametric fields -- Hilbert-like spaces over Krull valued fields -- Compact operators on non-classical Hilbert spaces -- Locally convex spaces over non-archimedean valued fields -- Finite-dimensional orthocomplemented subspaces in p-adic normed spaces -- Systems of differential equations over valued fields -- Bi-analytic elements and partial isometries of hyperbolic space -- 1. Introduction. -- 2. Preliminaries. -- 3. Hyperbolic Space. -- 4. Distance δ on Cp U HP. -- 5. Geometry of Cp U Hp. -- 6. Partial isometries of Hp. -- 7. Open affinoids and circular filters. -- 8. Rational maps. -- 9. Local isometries induced by rational maps. -- 10. Extension of an analytic element.

11. Composition of analytic elements and bi-analytic elements. -- 12. Global properties of bi-analytic elements. -- 13. Appendix: analytic elements and ends. -- References -- Analytic roots of solutions of p-adic differential equations -- Measure theory and integration on the Levi-Civita field -- On block basic sequences in non-archimedean Fréchet spaces -- Dynamical systems in unramified or totally ramified extensions of the p-adic number field -- p-adic analysis and the calculus of finite differences.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.