Advances in Non-Archimedean Analysis.

Intro -- Contents -- Preface -- Remembering Nicole De Grande-De Kimpe (1936-2008) -- Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure -- q-difference equations in ultrametric fields -- Primitives of p-adic meromorphic functions -- Existence of GCD's and factorization in rings of non-Archimedean entire functions -- The radius of convergence function for first order differential equations -- The Lipschitz condition for rational functions on ultrametric valued fields -- Differential and maximal ideals of the ultrametric Corona algebra -- Linear topologies on non-Archimedean function spaces -- On maximal closed ideals in topological algebras of continuous vector-valued functions over non-Archimedean valued fields -- Perturbations of bounded linear operators on orthomodular Hilbertian spaces -- On some geometrical properties of linear subspaces of l∞ -- The geometry of p-adic fractal strings: A comparative survey -- 1. Introduction -- 2. Archimedean vs. Nonarchimedean Cantor Set and String -- 3. p-Adic Fractal Strings -- 4. Nonarchimedean Self-similar Strings -- 5. Concluding Comments -- References -- Identities and congruences for Genocchi numbers -- Toward an ultrametric calculus in a field K with an infinite rank valuation -- Extending the multiplication of a totally ordered group to its completion -- Norm Hilbert spaces with uncountable orthogonal basis -- Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field -- Some p-adic q-difference equations on C(Zp,K).

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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.