(DFS)-spaces of holomorphic functions invariant under differentiation

DOI10.1016/J.JMAA.2004.03.030zbMath1068.46017OpenAlexW1988594899MaRDI QIDQ1883359

Sergej N. Melikhov

Publication date: 12 October 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.03.030

zbMATH Keywords

Laplace transform(DFS)-spaceduality of spaces of holomorphic functionsholomorphic functions of polynomial growthweighted Fréchet space of entire functions

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Spaces of bounded analytic functions of one complex variable (30H05) Laplace transform (44A10) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11)

Related Items (4)

Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains ⋮ The Cesàro operator on Korenblum type spaces of analytic functions ⋮ 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

Cites Work

• A Beurling-type theorem
• Space of analytic functions with prescribed growth near the boundary
• SPACES OF ANALYTIC FUNCTIONS OF PRESCRIBED GROWTH NEAR THE BOUNDARY
• Representing systems
• ON EXPANSION OF ANALYTIC FUNCTIONS IN EXPONENTIAL SERIES
• An extremal plurisubharmonic function associated to a convex pluricomplex Green function with pole at infinity.
• Notions of convexity
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