On an explicit construction of weakly sufficient sets for the function algebraA−∞(Ω)

DOI10.1080/17476930903030028zbMath1202.32005OpenAlexW2114310679MaRDI QIDQ3396435

Young-Jun Choi, Le Hai Khoi, Kang-Tae Kim

Publication date: 18 September 2009

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

Full work available at URL: https://doi.org/10.1080/17476930903030028

zbMATH Keywords

function algebraweakly sufficient setregular inductive limit

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (6)

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 ⋮ Convolution operators in \(A^{-\infty}\) for convex domains ⋮ On the duality between \(A^{-\infty }(D)\) and \(A^{-\infty }_D\) for convex domains ⋮ Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series ⋮ Mutual dualities betweenA^−∞(Ω) and for lineally convex domains

Cites Work

• Biholomorphic mappings and the \(\overline\partial\)-problem
• Weakly sufficient sets for \(A^{-\infty}(\mathbb D)\)
• Sampling sequences for \(A^{-\infty}\)
• Representation of harmonic functions in the Lie ball by Dirichlet series
• Interpolation by holomorphic functions in the unit ball with polynomial growth
• Sampling sets and sufficient sets for \(A^{-\infty}\)
• Projective and injective limits of weakly compact sequences of locally convex spaces
• A^–∞-interpolation in the ball

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