Advances in Non-Archimedean Analysis
This volume contains papers based on lectures given at the Eleventh International Conference on $p$-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France. The articles collected here feature recent developments in various areas of non-Archimedean analysis: Hilbert...
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| Hlavní autori: | , , |
|---|---|
| Médium: | E-kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Providence, Rhode Island
American Mathematical Society
2011
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| Vydanie: | 1 |
| Edícia: | Contemporary Mathematics |
| Predmet: | |
| ISBN: | 0821852914, 9780821852910 |
| ISSN: | 0271-4132, 1098-3627 |
| On-line prístup: | Získať plný text |
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Obsah:
- 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 -- <inline-formula content-type="math/mathml"> q q </inline-formula>-difference equations in ultrametric fields -- Primitives of <inline-formula content-type="math/mathml"> p p </inline-formula>-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 <inline-formula content-type="math/mathml"> l ∞<!-- ∞ --> l^\infty </inline-formula> -- The geometry of <inline-formula content-type="math/mathml"> p p </inline-formula>-adic fractal strings: A comparative survey -- Identities and congruences for Genocchi numbers -- Toward an ultrametric calculus in a field <inline-formula content-type="math/mathml"> K K </inline-formula> 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 <inline-formula content-type="math/mathml"> p p </inline-formula>-adic <inline-formula content-type="math/mathml"> q q </inline-formula>-difference equations on <inline-formula content-type="math/mathml"> C ( Z p , K ) \mathcal {C}(\mathbb {Z}_p,K) </inline-formula>
- 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)