# zbMATH — the first resource for mathematics

Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains. (English. French summary) Zbl 1239.47024
The main goal of the paper is to study a problem of extension of solutions of convolution type equations for spaces of holomorphic functions in convex domains of the complex plane with polynomial growth near the boundary.

##### MSC:
 47B38 Linear operators on function spaces (general) 32A38 Algebras of holomorphic functions of several complex variables 44A35 Convolution as an integral transform 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
Full Text:
##### References:
 [1] Abanin, A.V.; Khoi, Le Hai, On the duality between $$A^{- \infty}(D)$$ and $$A_D^{- \infty}$$ for convex domains, C. R. acad. sci. Paris, ser. I, 347, 863-866, (2009) · Zbl 1177.46016 [2] Abanin, A.V.; Khoi, Le Hai, Dual of the function algebra $$A^{- \infty}(D)$$ and representation of functions in Dirichlet series, Proc. amer. math. soc., 138, 3623-3635, (2010) · Zbl 1205.32004 [3] Abanin, A.V.; Ishimura, R.; Khoi, Le Hai, Surjectivity criteria for convolution operators in $$A^{- \infty}$$, C. R. acad. sci. Paris, ser. I, 348, 253-256, (2010) · Zbl 1190.32001 [4] A.V. Abanin, R. Ishimura, Le Hai Khoi, Convolution operators in $$A^{- \infty}$$ for convex domains, Ark. Mat., doi:10.1007/s11512-011-0146-4, in press. · Zbl 1254.32009 [5] Andronikof, E., Intégrales de nilsson et faisceaux constructibles, Bull. soc. math. France, 120, 51-85, (1992) · Zbl 0761.32006 [6] Berenstein, C.A.; Gay, R.; Vidras, A., Division theorems in spaces of entire functions with growth conditions and their applications to PDE of infinite order, Publ. res. inst. math. sci., 30, 5, 745-765, (1994) · Zbl 0842.32001 [7] Bony, J.M.; Schapira, P., Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. math., 17, 95-105, (1972) · Zbl 0225.35008 [8] Edwards, R.E., Functional analysis. theory and applications, (1965), Holt · Zbl 0182.16101 [9] Epifanov, O.V., On solvability of the nonhomogeneous Cauchy-Riemann equation in classes of functions that are bounded with weights or system of weights, Math. notes, 51, 54-60, (1992) [10] Hörmander, L., An introduction to complex analysis in several variables, (1966), North-Holland Publ. Comp. · Zbl 0138.06203 [11] Ishimura, R.; Okada, J., Sur la condition (S) de Kawai et la propriété de croissance régulière dʼune fonction sous-harmonique et dʼune fonction entière, Kyushu J. math., 48, 257-263, (1994) · Zbl 0815.32002 [12] Ishimura, R.; Okada, Y., The existence and the continuation of holomorphic solutions for convolution equations in tube domains, Bull. soc. math. France, 122, 413-433, (1994) · Zbl 0826.35144 [13] Kawai, T., On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. fac. sci. univ. Tokyo, sect. IA math., 17, 467-517, (1970) · Zbl 0212.46101 [14] Kiselman, C.O., Prolongement des solutions dʼune équation aux dérivées partielles à coefficients constants, Bull. soc. math. France, 97, 329-356, (1969) · Zbl 0189.40502 [15] Krasičkov-Ternovskiĭ, I.F., Invariant subspaces of analytic functions. analytic continuation, Math. USSR izv., 7, 933-947, (1973) · Zbl 0343.46019 [16] Krivosheev, A.S., A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane, Izv. math., 68, 43-76, (2004) · Zbl 1069.30002 [17] Krivosheev, A.S.; Napalkov, V.V., Complex analysis and convolution operators, Russian math. surveys, 47, 1-56, (1992) · Zbl 0801.46051 [18] Lelong, P.; Gruman, L., Entire functions of several complex variables, (1986), Springer-Verlag · Zbl 0583.32001 [19] Levin, B.Ya., Lectures on entire functions, Transl. math. monogr., vol. 150, (1996), AMS · Zbl 0856.30001 [20] Martineau, A., Distribution et valeurs au bord des fonctions holomorphes, (), 439-582, Œuvre de André Martineau [21] Meise, R.; Vogt, D., Introduction to functional analysis, (1997), Oxford University Press [22] Melikhov, S.N., (DFS)-spaces of holomorphic functions invariant under differentiation, J. math. anal. appl., 297, 577-586, (2004) · Zbl 1068.46017 [23] Sébbar, A., Prolongement des solutions holomorphes de certains opérateurs différentiels dʼordre infini à coefficients constants, (), 199-220 · Zbl 0451.32009 [24] Yulmukhametov, R.S., Approximation of subharmonic functions, Anal. math., 11, 257-282, (1985), (in Russian) · Zbl 0594.31005 [25] Zerner, M., Domaines dʼholomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. acad. sci. Paris, 272, 1646-1648, (1971) · Zbl 0213.37004 [26] Zharinov, V.V., Compact families of locally convex topological vector spaces, Fréchet-Schwartz and dual Fréchet-Schwartz spaces, Russian math. surveys, 34, 105-143, (1979) · Zbl 0443.46002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.