Cauchy-Fantappiè transformation and mutual dualities between \(A^{- \infty}(\varOmega)\) and \(A^\infty(\tilde {\varOmega})\) for lineally convex domains

DOI10.1016/J.CRMA.2011.10.013zbMath1257.32004OpenAlexW2055282989MaRDI QIDQ650857

Le Hai Khoi, Alexander V. Abanin

Publication date: 7 December 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2011.10.013

zbMATH Keywords

dualityCauchy-Fantappiè kernellineally convex domainstrictly starlike domain

Mathematics Subject Classification ID

Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Topological linear spaces of continuous, differentiable or analytic functions (46E10)

Related Items (3)

Analytic description of the spaces dual to spaces of holomorphic functions of given growth on Carathéodory domains ⋮ Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth ⋮ Mutual dualities betweenA^−∞(Ω) and for lineally convex domains

Cites Work

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• Sampling sequences for \(A^{-\infty}\)
• Sampling sets and sufficient sets for \(A^{-\infty}\)
• Complex convexity and analytic functionals
• 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)
• Sufficient Sets for Some Spaces of Entire Functions

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