@article{BSMF_1994__122_3_413_0, author = {Ishimura, Ryuichi and Okada, Yasunori}, title = {The existence and the continuation of holomorphic solutions for convolution equations in tube domains}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {413--433}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {122}, number = {3}, year = {1994}, doi = {10.24033/bsmf.2240}, mrnumber = {96f:32013}, zbl = {0826.35144}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/bsmf.2240/} }
TY - JOUR AU - Ishimura, Ryuichi AU - Okada, Yasunori TI - The existence and the continuation of holomorphic solutions for convolution equations in tube domains JO - Bulletin de la Société Mathématique de France PY - 1994 SP - 413 EP - 433 VL - 122 IS - 3 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2240/ DO - 10.24033/bsmf.2240 LA - en ID - BSMF_1994__122_3_413_0 ER -
%0 Journal Article %A Ishimura, Ryuichi %A Okada, Yasunori %T The existence and the continuation of holomorphic solutions for convolution equations in tube domains %J Bulletin de la Société Mathématique de France %D 1994 %P 413-433 %V 122 %N 3 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/bsmf.2240/ %R 10.24033/bsmf.2240 %G en %F BSMF_1994__122_3_413_0
Ishimura, Ryuichi; Okada, Yasunori. The existence and the continuation of holomorphic solutions for convolution equations in tube domains. Bulletin de la Société Mathématique de France, Tome 122 (1994) no. 3, pp. 413-433. doi : 10.24033/bsmf.2240. http://archive.numdam.org/articles/10.24033/bsmf.2240/
[1] Fonctions plurisousharmoniques, différence de deux fonctions plurisousharmoniques de type exponentiel, C. R. Acad. Sc., Paris, t. 252, 1961, p. 499-500. | MR | Zbl
. -[2] Existence and continuation of holomorphic solutions of differential equations of infinite order, Adv. in Math., t. 72, 1988, p. 261-283. | MR | Zbl
. -[3] Division theorems in the spaces of entire functions with growth conditions and their applications to PDE of infinite order, preprint.
, and . -[4] A remark on «convolutors in spaces of holomorphic functions», Lecture Notes in Math., t. 1276, 1987, p. 276-280. | MR | Zbl
and . -[5] Solutions of convolution equations in convex sets, Amer. J. Math., t. 109, 1987, p. 521-543. | MR | Zbl
and . -[6] Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. Math., t. 17, 1972, p. 95-105. | MR | Zbl
et . -[7] Solvability of convolution equations in convex domains, Soviet Math. Notes, t. 15, 1974, p. 472-477. | MR | Zbl
. -[8] On the surjectivity of convolution operators in complex domains, Soviet Math. Notes, t. 16, 1974, p. 837-841. | MR | Zbl
. -[9] Criteria for a convolution to be epimorphic in arbitrary regions of the complex plaine, Soviet Math. Notes, t. 31, 1982, p. 354-359. | MR | Zbl
. -[10] On the addition of the indicators of entire and subharmonic functions of several variables, Mat. Sb., t. 105, 147, 1978, p. 128-140. | MR | Zbl
. -[11] Generarized Fourier expansions for zero-solutions of surjective convolution operators on Dʹ (ℝ) and Dʹω (ℝ), preprint.
and . -[12] On the range of convolution operators, Ann. of Math., t. 76, 1962, p. 148-170. | MR | Zbl
. -[13] An introduction to complex analysis in several variables. - Van Nostrand Reinhold, 1966. | Zbl
. -[14] Théorèmes d'existence et d'approximation pour les équations aux dérivées partielles linéaires d'ordre infini, Publ. RIMS Kyoto Univ., t. 32, 1980, p. 393-415. | MR | Zbl
. -[15] Existence locale de solutions holomorphes pour les équations différentielles d'ordre infini, Ann. Inst. Fourier, Grenoble, t. 35, 3, 1985, p. 49-57. | Numdam | MR | Zbl
. -[16] A remark on the characteristic set for convolution equations, Mem. Fac. Sci. Kyushu Univ., t. 46, 1992, p. 195-199. | MR | Zbl
. -[17] Introduction to hyperfunctions. - Kluwer Acad. Publ., 1988. | MR | Zbl
. -[18] Sheaves on manifolds. - Grundlehren Math. Wiss., Berlin, Heidelberg, New York, Springer, 292, 1990. | MR | Zbl
and . -[19] On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., t. 17, 1970, p. 467-517. | MR | Zbl
. -[20] Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France, t. 97, 1969, p. 329-356. | Numdam | MR | Zbl
. —[21] On solutions of some functional equations in classes of functions analytic in convex domains, Mat. USSR Sb., t. 4, 1968, p. 203-211.
. —[22] The existence of an analytic solution of an infinite order differential equation and the nature of its domain of analyticity, Mat. USSR Sb., t. 9, 1969, p. 53-71. | Zbl
. —[23] Convolution equations in the complex domain, Mat. Sb., t. 55, 1985, p. 171-193. | Zbl
. —[24] Entire functions of several complex variables. — Grundlehren Math. Wiss., Berlin, Heidelberg, New York, Springer 282, 1986. | MR | Zbl
and . —[25] Distributions of zeros of entire functions, Transl. Math. Mono. Amer. Math. Soc., Providence, Rhode Island 5, 1964.
.—[26] Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier, t. 6, 1955-1956, p. 271-354. | Numdam | MR | Zbl
.—[27] Convolutors in spaces of holomorphic functions, Lecture Notes in Math., t. 1276, 1987, p. 253-275. | MR | Zbl
and .—[28] Convex univalent functions and continuous linear right inverses, J. Funct. Anal., t. 103, 1992, p. 85-103. | MR | Zbl
.—[29] Convolution equations in spaces of functions holomorphic in convex domains and on convex compacta in ℂn, Soviet Math. Notes, t. 16, 1974, p. 846-851. | Zbl
.—[30] On epimorphicity of a convolution operator in a convex domains in ℂl, Math. USSR Sb., t. 60, 1988, p. 347-364. | MR | Zbl
. —[31] Convolution equations in convex domains of ℂn, in Compl. Anal. and Appl. '87, Sofia, 1989, p. 360-364. | MR
.—[32] Convolution equations in multidimensional spaces, Mat. Zametki, t. 25, 1979, p. 761-774. | MR | Zbl
.—[33] Solvability of convolution operators, to appear in Publ. RIMS Kyoto Univ., t. 30, 1994. | MR | Zbl
.—[34] Prolongement des solutions holomorphes de certains opérateurs différentiels d'ordre infini à coefficients constants, Séminaire Lelong-Skoda, Lecture Notes in Math., Berlin, Heidelberg, New York, Springer, t. 822, 1980, p. 199-220. | MR | Zbl
.—[35] Equations of convolution type in spaces of analytic functionals, Math. USSR Izv., t. 11, 1977, p. 361-374. | Zbl
.—[36] Interpolation and division problems in spaces of entire functions with growth conditions and their applications, Doct. Diss., Univ. of Maryland, 1992.
.—[37] Domaines d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C.R. Acad. Sc., Paris, t. 272, 1971, p. 1646-1648. | MR | Zbl
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