L’équation $\overline{\partial }$ dans les ouverts pseudo-convexes des espaces DFN

 Access to full text

 Full (PDF)

1. [1] BONIC (R.) et FRAMPTON (J.). — Smooth functions on Banach manifolds, journal of Math. and Mech., t. 15, 1966, p. 877-898. Zbl0143.35202MR33 #6647
2. [2] COLOMBEAU (J. F.). — Sur les applications différentiables et analytiques au sens de J. S. e Silva. Portugaliae Mathematica, vol. 36, fasc. 2, 1977, p. 103-118. Zbl0449.46039MR81g:46054
3. [3] COLOMBEAU (J. F.). — Spaces of Cx mappings in infinitely many dimension and applications, Bordeaux, 1977 (preprint). 
4. [4] COLOMBEAU (J. F.) et MFISI (R.). — Cx functions on locally convex and on bornological vector spaces. Functional Analysis. Holomorphy and Approximation Theory, [MACHADO (S.)], Ed., Lecture Notes in Math. Springer, n° 843, 1981, p. 195-216. Zbl0494.46042
5. [5] COLOMBEAU (J. F.) et PERROT (B.). — Reflexivity and kernels in infinite dimensional holomorphy, Portugaliae Mathematica, vol. 46, n° 3-4, 1977, p. 291-300. Zbl0441.46021MR82e:46063
6. [6] COLOMBEAU (J. F.) et PERROT (B.). — The ∂ equation in DFN spaces, Journal of Math. Analysis and Application, vol. 78, n° 2, 1980, p. 466-487. Zbl0455.46045MR82c:32019
7. [7] COLOMBEAU (J. F.), GAY (R.) et PERROT (B.). — Division by holomorphic functions and convolution equations in infinite dimensions. Transactions of the A.M.S., vol. 264, n° 2, 1981, p. 381-391. Zbl0494.46052MR82e:46060
8. [8] GRUMAN (L.). — The Lévi problem in certain infinite dimensional vector spaces, Illinois Journal of Math., t. 18, 1974, p. 20-26. Zbl0276.32017MR50 #993
9. [9] GRUMAN (L.) et KISELMAN (C. O.). — Le problème de Lévi dans les espaces de Banach à base, C. R. Acad. Sc. Paris, t. 274, série A, 1972, p. 1296-1298. Zbl0243.32017MR45 #3759
10. [10] HENRICH (C. J.). — The ∂ equation with polynomial growth on a Hilbert space, Duke Math. Journal, vol. 40, n° 2, 1973, p. 279-306. Zbl0261.35063MR47 #9279
11. [11] HOGBE-NLEND (H.). — Théorie des Bornologies et Applications, Lecture Notes in Math., n° 213, Springer, 1971. Zbl0225.46005MR58 #30002
12. [12] HOGBE-NLEND (H.). — Bornologies and Functional Analysis, North Holland Math. Studies, 26, 1978. Zbl0359.46004MR58 #17774
13. [13] HORMANDER (L.). — An introduction to complex analysis in several variable, North Holland, 1973. Zbl0271.32001MR49 #9246
14. [14] MAZET (P.). — Communication personnelle, avril 1980. 
15. [15] NOVERRAZ (P.). — Approximation of holomorphic or plurisubharmonic function in certain Banach spaces. Proceedings on Infinite Dimensional holomorphy, Lecture Notes in Math., n° 364, Springer, 1974, p. 178-18. Zbl0284.46018MR52 #15008
16. [16] NOVERRAZ (P.). — Pseudo convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North Holland Math Studies, t. 3, 1973. Zbl0251.46049MR50 #10814
17. [17] PIETSCH (A.). — Nuclear Locally convex spaces, Ergebnisse der math., t. 66, Springer, 1972. Zbl0236.46001MR50 #2853
18. [18] RABOIN (P.). — Le problème du ∂ sur un espace de Hilbert, Séminaire Lelong-Skoda, 1976-1977, Lecture Notes in Math., n° 694, Springer, 1978, p. 214-227. Zbl0418.32017MR80g:32035
19. [19] RABOIN (P.). — The ∂ equation on a Hilbert space and some applications Advances in Holomorphy, BARROSO (J. A.), Ed., North Holland Math Studies, t. 34, 1979, p. 713-734. Zbl0421.46041
20. [20] RABOIN (P.). — Le problème du ∂ sur un espace de Hilbert, Bulletin de la Soc. Math. de France, t. 107, 1979, p. 225-240. Zbl0414.46030MR80i:32052
21. [21] RAPP (A.). — L'équation ∂ avec décroissance au bord sur certains ouverts convexes d'un espace de Banach, Bulletin de la Soc. Math. de France, Suppl. Mémoire, n° 46, 1976, p. 67-72. Zbl0375.35045MR57 #6509
22. [22] SCHOTTENLOHER (M.). — The Lévi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition, Annales de l'Institut Fourier, vol. 26, n° 4, 1976, p. 207-237. Zbl0309.32013MR58 #1262

1. Joji Kajiwara, Kwang Ho Shon, Miki Tsuji, Localization of global existence of holomorphic solutions of holomorphic differential equations with infinite dimensional parameter