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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| Médium: | E-kniha |
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Providence, Rhode Island
American Mathematical Society
2011
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| Vydání: | 1 |
| Edice: | Contemporary Mathematics |
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| ISBN: | 0821852914, 9780821852910 |
| ISSN: | 0271-4132, 1098-3627 |
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| Abstract | 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 and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra. |
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| AbstractList | 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 and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra. |
| Author | Escassut, Alain Diarra, Bertin Araujo-Gomez, Jesus |
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| Editor | Escassut, Alain Diarra, Bertin Araujo-Gomez, Jesus |
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| Snippet | 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,... |
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| SubjectTerms | Congresses De Grande-De Kimpe, N p-adic analysis Topological fields |
| TableOfContents | 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) |
| Title | Advances in Non-Archimedean Analysis |
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