On the ultrametric Stone-Weierstrass theorem and Mahler's expansion

DOI10.5802/jtnb.345zbMath1031.46086OpenAlexW1977455527MaRDI QIDQ1396431

Jean-Luc Chabert, Paul-Jean Cahen

Publication date: 30 June 2003

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2002__14_1_43_0

zbMATH Keywords

ultrametricStone-Weierstrass theorems

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) General theory of topological algebras (46H05)

Related Items (10)

Adelic versions of the Weierstrass approximation theorem ⋮ Groups of diffeomorphisms and geometric wraps of manifolds over ultra-normed fields ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ Mahler's polynomial approximation for odd and even \(p\)-adic functions ⋮ Paul-Jean Cahen (1946–2019) ⋮ Regular subsets of valued fields and Bhargava's \(v\)-orderings ⋮ Minimal Generating Sets for the D-Algebra Int(S, D) ⋮ Prüfer domains of integer-valued polynomials on a subset ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis

Cites Work

• Completely continuous endomorphisms of \(p\)-adic Banach spaces
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• On a theorem of R. Gilmer
• Continuous functions on discrete valuation rings
• \(p\)-adic Banach spaces and families of modular forms
• Interpolation domains
• Integer-Valued Polynomials
• An Interpolation Series for Continuous Functions of a p-adic Variable.
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Continuous functions on compact subsets of local fields
• Interpolation series for continuous functions on π-adic completions of GF(q, x)
• Topological Rings
• The Weierstrass Theorem in Fields with Valuations
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