The existence and the continuation of holomorphic solutions for convolution equations in tube domains
Ishimura, Ryuichi ; Okada, Yasunori
Bulletin de la Société Mathématique de France, Tome 122 (1994), p. 413-433 / Harvested from Numdam
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@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},
     volume = {122},
     year = {1994},
     pages = {413-433},
     doi = {10.24033/bsmf.2240},
     mrnumber = {96f:32013},
     zbl = {0826.35144},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 413-433. doi : 10.24033/bsmf.2240. http://gdmltest.u-ga.fr/item/BSMF_1994__122_3_413_0/

[1] Avanissian (V.). - Fonctions plurisousharmoniques, différence de deux fonctions plurisousharmoniques de type exponentiel, C. R. Acad. Sc., Paris, t. 252, 1961, p. 499-500. | MR 23 #A1841 | Zbl 0173.39605

[2] Aoki (T.). - Existence and continuation of holomorphic solutions of differential equations of infinite order, Adv. in Math., t. 72, 1988, p. 261-283. | MR 90e:35007 | Zbl 0702.35253

[3] Berenstein (C.A.), Gay (R.) and Vidras (A.). - Division theorems in the spaces of entire functions with growth conditions and their applications to PDE of infinite order, preprint.

[4] Berenstein (C.A.) and Struppa (D.C.). - A remark on «convolutors in spaces of holomorphic functions», Lecture Notes in Math., t. 1276, 1987, p. 276-280. | MR 89e:32004 | Zbl 0628.42009

[5] Berenstein (C.A.) and Struppa (D.C.). - Solutions of convolution equations in convex sets, Amer. J. Math., t. 109, 1987, p. 521-543. | MR 89c:32006 | Zbl 0628.46036

[6] Bony (J.M.) et Schapira (P.). - Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. Math., t. 17, 1972, p. 95-105. | MR 49 #3305 | Zbl 0225.35008

[7] Epifanov (O.V.). - Solvability of convolution equations in convex domains, Soviet Math. Notes, t. 15, 1974, p. 472-477. | MR 51 #3946 | Zbl 0322.46056

[8] Epifanov (O.V.). - On the surjectivity of convolution operators in complex domains, Soviet Math. Notes, t. 16, 1974, p. 837-841. | MR 52 #8431 | Zbl 0331.47026

[9] Epifanov (O.V.). - Criteria for a convolution to be epimorphic in arbitrary regions of the complex plaine, Soviet Math. Notes, t. 31, 1982, p. 354-359. | MR 84h:30082 | Zbl 0509.47042

[10] Favorov (Yu). - On the addition of the indicators of entire and subharmonic functions of several variables, Mat. Sb., t. 105, 147, 1978, p. 128-140. | MR 57 #16652 | Zbl 0374.32001

[11] Franken (U.) and Meise (R.). - Generarized Fourier expansions for zero-solutions of surjective convolution operators on Dʹ (ℝ) and Dʹω (ℝ), preprint.

[12] Hörmander (L.). - On the range of convolution operators, Ann. of Math., t. 76, 1962, p. 148-170. | MR 25 #5379 | Zbl 0109.08501

[13] Hörmander (L.). - An introduction to complex analysis in several variables. - Van Nostrand Reinhold, 1966. | Zbl 0138.06203

[14] Ishimura (R.). - 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 82f:35048 | Zbl 0459.35015

[15] Ishimura (R.). - 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 87c:35005 | Zbl 0544.35085

[16] Ishimura (R.). - A remark on the characteristic set for convolution equations, Mem. Fac. Sci. Kyushu Univ., t. 46, 1992, p. 195-199. | MR 93k:58210 | Zbl 0773.32006

[17] Kaneko (A.). - Introduction to hyperfunctions. - Kluwer Acad. Publ., 1988. | MR 90m:32017 | Zbl 0687.46027

[18] Kashiwara (M.) and Schapira (P.). - Sheaves on manifolds. - Grundlehren Math. Wiss., Berlin, Heidelberg, New York, Springer, 292, 1990. | MR 92a:58132 | Zbl 0709.18001

[19] 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., t. 17, 1970, p. 467-517. | MR 45 #7252 | Zbl 0212.46101

[20] Kiselman (C.O.). — Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France, t. 97, 1969, p. 329-356. | Numdam | MR 42 #2161 | Zbl 0189.40502

[21] KorobeĬNik (Yu.F.). — On solutions of some functional equations in classes of functions analytic in convex domains, Mat. USSR Sb., t. 4, 1968, p. 203-211.

[22] KorobeĬNik (Yu.F.). — 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 0223.34015

[23] KorobeĬNik (Yu.F.). — Convolution equations in the complex domain, Mat. Sb., t. 55, 1985, p. 171-193. | Zbl 0587.45006

[24] Lelong (P.) and Gruman (L.). — Entire functions of several complex variables. — Grundlehren Math. Wiss., Berlin, Heidelberg, New York, Springer 282, 1986. | MR 87j:32001 | Zbl 0583.32001

[25] Levin (B.Ja).— Distributions of zeros of entire functions, Transl. Math. Mono. Amer. Math. Soc., Providence, Rhode Island 5, 1964.

[26] Malgrange (B.).— 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 19,280a | Zbl 0071.09002

[27] Méril (A.) and Struppa (D.C.).— Convolutors in spaces of holomorphic functions, Lecture Notes in Math., t. 1276, 1987, p. 253-275. | MR 89e:32003 | Zbl 0628.42008

[28] Momm (S.).— Convex univalent functions and continuous linear right inverses, J. Funct. Anal., t. 103, 1992, p. 85-103. | MR 93m:30057 | Zbl 0771.46016

[29] Morzhakov (V.V.).— 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 0322.45010

[30] Morzhakov (V.V.). — On epimorphicity of a convolution operator in a convex domains in ℂl, Math. USSR Sb., t. 60, 1988, p. 347-364. | MR 89b:32007 | Zbl 0678.46032

[31] Morzhakov (V.V.).— Convolution equations in convex domains of ℂn, in Compl. Anal. and Appl. '87, Sofia, 1989, p. 360-364. | MR 1127654

[32] Napalkov (V.V.).— Convolution equations in multidimensional spaces, Mat. Zametki, t. 25, 1979, p. 761-774. | MR 80m:32003 | Zbl 0403.45005

[33] Okada (Y.).— Solvability of convolution operators, to appear in Publ. RIMS Kyoto Univ., t. 30, 1994. | MR 94m:46077 | Zbl 0808.46057

[34] Sébbar (A.).— 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 82f:35049 | Zbl 0451.32009

[35] TkaČEnko (T.A.).— Equations of convolution type in spaces of analytic functionals, Math. USSR Izv., t. 11, 1977, p. 361-374. | Zbl 0378.45004

[36] Vidras (A.).— Interpolation and division problems in spaces of entire functions with growth conditions and their applications, Doct. Diss., Univ. of Maryland, 1992.

[37] Zerner (M.).— Domaines d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C.R. Acad. Sc., Paris, t. 272, 1971, p. 1646-1648. | MR 55 #5995 | Zbl 0213.37004