Ensembles pics pour A (D)
Annales de l'Institut Fourier, Volume 29 (1979) no. 3, p. 171-200

Let D be a bounded strictly pseudoconvex domain in C n with smooth boundary D. Let A (D) be the class of functions analytic in D and continuous with all their derivatives in D ¯. Let N be a C -submanifold of D whose tangent space T p (N) lies in the maximal complex subspace of T p (D), for every pN. In this work, we show that every compact subset of N is a peak set for A (D).

Soit D un domaine borné strictement pseudoconvexe dans C n à frontière régulière D. On montre que tout compact d’une sous-variété N de D dont l’espace tangent T p (N) en chaque point p de N est contenu dans le sous-espace complexe maximal de T p (D) est un ensemble pic pour A (D), la classe des fonctions analytiques dans D dont toutes les dérivées sont continues dans D ¯.

@article{AIF_1979__29_3_171_0,
     author = {Chaumat, Jacques and Chollet, Anne-Marie},
     title = {Ensembles pics pour $A^\infty (D)$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {29},
     number = {3},
     year = {1979},
     pages = {171-200},
     doi = {10.5802/aif.757},
     zbl = {0398.32004},
     mrnumber = {81c:32036},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1979__29_3_171_0}
}
Chaumat, Jacques; Chollet, Anne-Marie. Ensembles pics pour $A^\infty (D)$. Annales de l'Institut Fourier, Volume 29 (1979) no. 3, pp. 171-200. doi : 10.5802/aif.757. http://www.numdam.org/item/AIF_1979__29_3_171_0/

[1] V.I. Arnold, Les méthodes mathématiques de la mécanique classique, Editions MIR (1976), Moscou. | MR 57 #14033a | Zbl 0385.70001

[2] D. Burns, and E.L. Stout, Extending functions from submanifolds of the boundary, Duke Math. J., 43 (1976), 391-404. | MR 54 #3028 | Zbl 0328.32013

[3] G.B. Folland and J.J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton University Press (1972). | MR 57 #1573 | Zbl 0247.35093

[4] G.B. Folland and E.M. Stein, Estimates for the ∂b complex and analysis on the Heisenberg group, Com. Pure Appl. Math., 27 (1974), 429-522. | MR 51 #3719 | Zbl 0293.35012

[5] W. Guillemin, Géométrie symplectique et physique mathématique, Colloque Intern. C.N.R.S, Aix en Provence (1974).

[6] M. Hakim et N. Sibony, Ensembles pics dans des domaines strictement pseudoconvexes, Duke Math. J., 45 (1978), 601-617. | MR 80c:32007 | Zbl 0402.32008

[7] F.R. Harvey and R.O. Wells, Holomorphic approximation and hyperfunction theory on a C1 totally real submanifold of a complex manifold, Math. Ann., 197 (1972), 287-318. | MR 46 #9379 | Zbl 0246.32019

[8] G.M. Henkin, et A.E. Tumanov, C.R. Ecole d'été à Drogobytch (1974).

[9] S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag (1972), Appendice 1. | MR 50 #8360 | Zbl 0246.53031

[10] J.J. Kohn, Global regularity for ∂ on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc., 181 (1973), 273-292. | MR 49 #9442 | Zbl 0276.35071

[11] A. Nagel, Smooth zero sets and interpolation sets for some algebras of holomorphic functions on strictly pseudoconvex domains, Duke Math. J., 43 (1976), 323-348. | MR 56 #670 | Zbl 0343.32016

[12] W. Rudin, Peak interpolation sets of classe C1, Pacific J. Math., 75 (1978), 267-279. | MR 58 #6346 | Zbl 0383.32007

[13] A. Weinstein, Lectures on symplectic manifolds, Regional conference series in mathematics 29, Amer. Math. Soc. | Zbl 0406.53031