Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains

DOI10.1016/j.bulsci.2011.06.002zbMath1239.47024OpenAlexW2033582640MaRDI QIDQ661958

Le Hai Khoi, Ryuichi Ishimura, Alexander V. Abanin

Publication date: 11 February 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2011.06.002

zbMATH Keywords

holomorphic functionconvex domainconvolution equationextension of solutionsFourier-Borel transformation

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Linear operators on function spaces (general) (47B38) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (3)

Solvability of the inhomogeneous Cauchy-Riemann equation in projective weighted spaces ⋮ Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth ⋮ On the surjectivity of the convolution operator in spaces of holomorphic functions of a prescribed growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convolution operators in \(A^{-\infty}\) for convex domains
• Surjectivity criteria for convolution operators in \(A^{-\infty}\)
• (DFS)-spaces of holomorphic functions invariant under differentiation
• Division theorems in spaces of entire functions with growth conditions and their applications to PDE of infinite order
• On the duality between \(A^{-\infty }(D)\) and \(A^{-\infty }_D\) for convex domains
• Existence et prolongement des solutions holomorphes des équations aux dérivées partielles. (Existence and prolongation of the holomorphic solutions of partial differential equations)
• Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series
• COMPACT FAMILIES OF LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES, FRÉCHET-SCHWARTZ AND DUAL FRÉCHET-SCHWARTZ SPACES
• Intégrales de Nilsson et faisceaux constructibles
• INVARIANT SUBSPACES OF ANALYTIC FUNCTIONS. ANALYTIC CONTINUATION
• Complex analysis and convolution operators
• SUR LA CONDITON (S) DE KAWAI ET LA PROPRIÉTÉ DE CROISSANCE RÉGULIÈRE D'UNE FONCTION SOUS-HARMONIQUE ET D'UNE FONCTION ENTIÈRE
• The existence and the continuation of holomorphic solutions for convolution equations in tube domains
• A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane
• Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants
• Approximation of subharmonic functions

This page was built for publication: Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains