| Title:
|
Localization of global existence of holomorphic solutions of holomorphic differential equations with infinite dimensional parameter (English) |
| Author:
|
Kajiwara, Joji |
| Author:
|
Shon, Kwang Ho |
| Author:
|
Tsuji, Miki |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
687-700 |
| . |
| Category:
|
math |
| . |
| MSC:
|
32C35 |
| MSC:
|
32F15 |
| MSC:
|
32G34 |
| MSC:
|
32K99 |
| MSC:
|
32T99 |
| MSC:
|
34A20 |
| idZBL:
|
Zbl 0956.32016 |
| idMR:
|
MR1658241 |
| . |
| Date available:
|
2009-09-24T10:17:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127447 |
| . |
| Reference:
|
[1] H. Cartan: Idéaux de fonctions analytiques de $n$ complexes variables.Bull. Soc. Math. France. 78 (1950), 28–64. MR 0036848 |
| Reference:
|
[2] H. Cartan: Séminaire E.N.S..École Normare Supérieur, Paris, 1951/1952. |
| Reference:
|
[3] G. Coeuré: L’équation $\overline{\partial }u=F$ en dimension infinite.université Lille Publ. Int. 131, 1968, pp. 6–9. |
| Reference:
|
[4] J. Colombeau and B. Perri: The $\overline{\partial }$-equation in D.F.N. spaces.J. Math. Anal. Appl. 78-2 (1980), 466–87. MR 0601549 |
| Reference:
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[5] J. Colombeau and B. Perri: L’équation $\overline{\partial }$ dans les ouverts pseudo-convexes des espaces D.F.N..Bull. Soc. Math. France. 110 (1982), 15–26. MR 0662127, 10.24033/bsmf.1951 |
| Reference:
|
[6] S. Dineen: Sheaves of holomorphic functions on infinite dimensional vector spaces.Math. Ann. 202 (1973), 337–345. Zbl 0238.46022, MR 0330511, 10.1007/BF01433463 |
| Reference:
|
[7] S. Dineen: Cousin’s first problem on certain locally convex topological spaces.Acad. Brasil. Cienc. 48-1 (1976), 229–236. MR 0438376 |
| Reference:
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[8] L. Gruman: The Levi problem in certain infinite dimensional vector spaces.Illinois J. Math. 18 (1974), 20–26. Zbl 0276.32017, MR 0348495, 10.1215/ijm/1256051345 |
| Reference:
|
[9] S. Hitotumatu: Theorem of analytic functions of several complex variables.(1960), Baihuukan. (Japanese) |
| Reference:
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[10] J. Kajiwara: On an application of L. Ehrenpreis’ method to ordinary differential equations, Kōdai Math. Sem. Rep..15-2 (1963), 94–105. MR 0151658 |
| Reference:
|
[11] J. Kajiwara and L. Li: Localization of Global Existence of Holomorphic Solutions of Differential Equations with Complex Parameters.Proc. 4th Int. Coll. on Differential Equations, VSP (Utrecht), 1993, pp. 147–156. MR 1458393 |
| Reference:
|
[12] J. Kajiwara and Y. Mori: On the existence of global holomorphic solutions of differential equations with complex parameters.Czechoslovak Math. J. 24(199) (1974), 444–454. MR 0358871 |
| Reference:
|
[13] J. Kajiwara and K. H. Shon: Continuation and vanishing theorem for cohomology of infinite dimensional space.Pusan Kyôngnam Math. J. 1 (1993), 65–73. |
| Reference:
|
[14] Ph. Noverraz: Pseudo-Convéxité, Convéxité et Domaines d’Holomorphie en Dimension Infinie.North-Holland. Math. Studies 3 (1973). |
| Reference:
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[15] K. Oka: Sur les fonctions analytiques plusieurs variables: VII Sur quelques notions arithmétiques.Bull. Soc. math. France 78 (1950), 1–27. MR 0035831 |
| Reference:
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[16] K. Oka: Sur les fonctions analytiques plusieurs variables: IX Domaines finis sans point critique intérieur.Jap. J. Math. 23 (1953), 1–27. MR 0071089 |
| Reference:
|
[17] R. L. Soraggi: The $\overline{\partial }$-problem for a $(0,2)$-form in a D.F.N. space.J. Func. Anal. 98 (1991), 380–402. MR 1111575, 10.1016/0022-1236(91)90084-I |
| Reference:
|
[18] J. P. S$\grave{e}$rre: Quelques problémes globaux aux variétés de Stein.Coll. Plus. Var., Bruxelle (1953), 57–68. |
| Reference:
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[19] H. Suzuki: On the global existence of holomorphic solutions of $\partial u/\partial x_1 = f$.Sci. Rep. Tokyo Kyoiku Daigaku 11 (1972), 253–258. MR 0310457 |
| Reference:
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[20] I. Wakabayashi: Non existence of holomorphic solutions of $\partial u/\partial z_1 = f$.Proc. Jap. Acad. 44 (1968), 820–822. MR 0240330 |
| . |
