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A formula for interpolation and division in \({\mathbb C}^n\). (English) Zbl 0499.32013

32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
32D15 Continuation of analytic objects in several complex variables
32A38 Algebras of holomorphic functions of several complex variables
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables
Full Text: DOI EuDML
[1] Amar, E.: Extension de fonctions holomorphe et courants. Preprint Orsay 1980
[2] Berenstein, C.A., Taylor, B.A.: Interpolation problems in ? n with applications to harmonic analysis. J. Analyse Math.38 (1980) · Zbl 0464.42003
[3] Berenstein, C.A., Taylor, B.A.: On the geometry of interpolating varieties. Sem. Lelong-Skoda 1980-1981. Lecture Notes in Mathematics 919. Berlin, Heidelberg, New York: Springer 1982
[4] Berndtsson, B., Andersson, M.: Henkin-Ramirez formulas with weight factors. Ann. Inst. Fourier32, 3 (1982) · Zbl 0466.32001
[5] Fornaess, J.E.: Embedding strictly pseudoconvex domains in convex domains. Am. J. Math.98 (1976) · Zbl 0334.32020
[6] Henkin, G.M.: Integral representation of a function in a strictly pseudoconvex domain and applications to the \(\bar \partial \) -problem (Russian) Mat. Sb. (1982)
[7] Henkin, G.M.: Continuation of bounded holomorphic functions from submanifolds in general position to strictly pseudoconvex domains (Russian). Izv. Akad. Nauk. SSSR, Ser. Mat.36 (1972) · Zbl 0255.32008
[8] Henkin, G.M., Leiterer, J.: Global integral formulas for solving the \(\bar \partial \) -equation on Stein manifolds. Ann. Pol. Math. (to appear) · Zbl 0477.32020
[9] Hörmander, L.: An introduction to complex analysis in several variables. Amsterdam, Van Nostrand 1966 · Zbl 0138.06203
[10] Hörmander, L.: Generators for some rings of analytic functions. Bull. Am. Math. Soc.73 (1967) · Zbl 0172.41701
[11] Lelong, P.: Fonctions plurisousharmoniques et formes différentielles positives. London: Gordon and Breach 1968 · Zbl 0195.11603
[12] Nishimura, Y.: Problème d’extension dans la théorie des fonctions entiére d’ordre fini. J. Math. Kyoto Univ.20 (1980) · Zbl 0467.32008
[13] Palm, A.: Integral representation formulas on strictly pseudoconvex domains in Sein manifolds. Duke Math. J.43 (1976) · Zbl 0329.32004
[14] Ramirez de Arellao, E.: Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis. Math. Ann.184, 172 (1969) · Zbl 0189.09702
[15] Skoda, H.: Application des techniquesL 2 a la theorie des ideaux d’une algébre de fonctions holomorphes avec poids. Ann. Sci. Ecole Norm. Sup.5 (1972) · Zbl 0254.32017
[16] Stout, E.L.: An integral formula for holomorphic functions on strictly pseudoconvex hypersurfaces. Duke Math. J.42 (1975) · Zbl 0333.32003
[17] Yoshioka, T.: Cohomologie a estimationL 2 et extension des fonctions holomorphes avec controle de la croissance. Proc. Jpn. Acad.57 (1981) · Zbl 0506.32002
[18] Cornalba, M., Shiffman, B.: A counterexample to the ?Transcendental Bezov-problem?. Ann. Math.96 (1972) · Zbl 0244.32006
[19] Demailly, J.P.: Scindage holomorphe d’un morphisme de fibrés vectoriels semi-positifs avec estimationL 2. Sem. Lelong-Skoda 1980-81. Lecture Notes in Mathematics 919. Berlin, Heidelberg, New York: Springer 1982
[20] Hortmann, M.: Globale holomorphe Kerne zur Lösung der Cauchy-Riemannschen differentialgleichungen. Annals Math. Studies 100 Princeton: Princeton University Press 1981 · Zbl 0492.32020
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