Mutual dualities betweenA−∞(Ω) and for lineally convex domains

DOI10.1080/17476933.2012.699963zbMath1287.46034OpenAlexW1994688876MaRDI QIDQ2862977

Le Hai Khoi, Alexander V. Abanin

Publication date: 20 November 2013

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2012.699963

zbMATH Keywords

analytic functionallinearly convex domains(weakly) sufficient setsCauchy-Fantappie transformseries of partial fractions

Mathematics Subject Classification ID

Topological linear spaces of continuous, differentiable or analytic functions (46E10) Duality theory for topological vector spaces (46A20) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Holomorphic functions of several complex variables (32A10)

Related Items (3)

Approximation with rational interpolants in \(A^{-\infty}(D)\) for Dini domains ⋮ Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth ⋮ The Closure and the Interior of C-convex Sets

Cites Work

• Pre-dual of the function algebra \(A^{-\infty}(D)\) and representation of functions in Dirichlet series
• Cauchy-Fantappiè transformation and mutual dualities between \(A^{- \infty}(\varOmega)\) and \(A^\infty(\tilde {\varOmega})\) for lineally convex domains
• Biholomorphic mappings and the \(\overline\partial\)-problem
• Weakly sufficient sets for \(A^{-\infty}(\mathbb D)\)
• Sampling sequences for \(A^{-\infty}\)
• Interpolation by holomorphic functions in the unit ball with polynomial growth
• Sampling sets and sufficient sets for \(A^{-\infty}\)
• Sur la topologie des espaces de fonctions holomorphes
• Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series
• SETS OF UNIQUENESS, WEAKLY SUFFICIENT SETS AND SAMPLING SETS FOR A-∞(B)
• On an explicit construction of weakly sufficient sets for the function algebraA^−∞(Ω)
• INDUCTIVE AND PROJECTIVE TOPOLOGIES. SUFFICIENT SETS AND REPRESENTING SYSTEMS
• COMPACT FAMILIES OF LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES, FRÉCHET-SCHWARTZ AND DUAL FRÉCHET-SCHWARTZ SPACES
• ON A DUAL PROBLEM. II. APPLICATIONS TO $ LN^*$-SPACES AND OTHER QUESTIONS

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