On dense ideals in spaces of analytic functions
Annales de l'Institut Fourier, Volume 44 (1994) no. 5, pp. 1355-1366.

One proves the density of an ideal of analytic functions into the closure of analytic functions in a L p (μ)-space, under some geometric conditions on the support of the measure μ and the zero variety of the ideal.

On démontre la densité d’un idéal de fonctions analytiques dans l’adhérence dans L p (μ) de toutes les fonctions analytiques, sous des conditions géométriques sur le support de la mesure μ et sur la variété des zéros de l’idéal.

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Putinar, Mihai. On dense ideals in spaces of analytic functions. Annales de l'Institut Fourier, Volume 44 (1994) no. 5, pp. 1355-1366. doi : 10.5802/aif.1437. http://www.numdam.org/articles/10.5802/aif.1437/

[1] E. Amar, Cohomologie complexe et applications, J. London Math. Soc. (2), 29 (1984), 127-140. | MR | Zbl

[2] E. Bierstone and P.D. Milman, Ideals of holomorphic functions with C∞ boundary values on a pseudoconvex domain, Trans. Amer. Math. Soc., 304 (1987), 323-342. | MR | Zbl

[3] J. Chaumat and A.-M. Chollet, Ensembles pics pour A∞ (D), Ann. Inst. Fourier (Grenoble), 29-3 (1979), 171-200. | EuDML | Numdam | MR | Zbl

[4] J. Chaumat and A.-M. Chollet, Caractérisation et propriétés des ensembles localement pics de A∞ (D), Duke Math. J., 47 (1980), 763-787. | MR | Zbl

[5] R.G. Douglas and V. Paulsen, Hilbert modules over function algebras, Pitman Res. Notes Math. vol. 217, Longman Sci. Techn., Harlow, 1989. | MR | Zbl

[6] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. Math., 4 (1967), 118-138. | EuDML | MR | Zbl

[7] F.R. Harvey and R.O. Wells, Zero sets of nonnegative strictly plurisubharmonic functions, Math. Ann., 201 (1973), 165-170. | EuDML | Zbl

[8] G.M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb., 78 (1969), 611-632 ; Math. USSR Sb., 7 (1969), 597-616. | Zbl

[9] G.M. Henkin and J. Leiterer, Theory of functions on complex manifolds, Birkhäuser, Basel-Boston-Berlin, 1984. | Zbl

[10] J.J. Kohn, Global regularity for ∂ on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc., 181 (1973), 273-292. | MR | Zbl

[11] B. Malgrange, Ideals of differentiable functions, Oxford Univ. Press, Oxford, 1966.

[12] A. Nagel, On algebras of holomorphic functions with C∞-boundary values, Duke Math. J., 41 (1974), 527-535. | MR | Zbl

[13] M. Putinar and N. Salinas, Analytic transversality and Nullstellensatz in Bergman space, Contemp. Math., 137 (1992), 367-381. | MR | Zbl

[14] W. Rudin, Function theory in the unit ball of Cn, Springer, New York-Heidelberg-Berlin, 1980. | MR | Zbl

[15] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966.

[16] N. Sibony, Some aspects of weakly pseudoconvex domains, Proc. Symp. Pure Math., 52 (1991), 199-231. | MR | Zbl

[17] Y.T. Siu, Noetherianness of rings of holomorphic functions on Stein compact sets, Proc. Amer. Math. Soc., 21 (1969), 483-489. | MR | Zbl

[18] J.C. Tougeron, Idéaux de fonctions différentiables, Springer, Berlin et al., 1972. | MR | Zbl

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