zbMATH — the first resource for mathematics

Holomorphic approximation and hyperfunction theory on a C\(^1\) totally real submanifold of a complex manifold. (English) Zbl 0246.32019

32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
46F15 Hyperfunctions, analytic functionals
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
Full Text: DOI EuDML
[1] Bungart, L.: Holomorphic functions with values in locally convex spaces and applications to integral formulas. Trans. Amer. Math. Soc.111, 317-344 (1964). · Zbl 0142.33902
[2] ?irka, E. M.: Approximation by holomorphic functions on smooth submanifolds in ?n. Mat. Sbornik,78, (120) (1969); AMS Translation: Math. USSR Sbornik7, 95-114 (1969).
[3] Grauert, H.: On Levi’s problem and the imbedding of real-analytic manifolds. Ann. of Math.68, 460-472 (1958). · Zbl 0108.07804
[4] ?? Lieb, I.: Das Ramiresche Integral und die Lösung der Gleichung 318-2f=? Bereich der beschränkten Formen (Proceedings of Conference on Complex Analysis, Rice Univ., 1969). Rice Univ. Studies56 (2), 26-50 (1970).
[5] Harvey, R.: Hyperfunctions and linear partial differential equations. Stanford, 1966 (thesis).
[6] ?? The theory of hyperfunctions on totally real subsets of a complex manifold with applications to extension problems. Am. J. Math.91, 853-873 (1969). · Zbl 0202.36602
[7] ?? Wells, R. O., Jr.: Holomorphic approximation on totally real submanifolds of a complex manifold. Bull. Amer. Math. Soc.77, 824-828 (1971). · Zbl 0219.32010
[8] Henkin, G. M.: Integral representations of functions in strictly pseudo-convex domains and some applications. Math. USSR Sbornik7, 597-615 (1969); Translated from: Mat. Sbornik78, 120 (1969). · Zbl 0208.35102
[9] – Integral representations of functions in strongly pseudo-convex domains and applications to the \(\overline \partial \) -problem. Mat. Sbornik82, (124), 300-308 (Russian).
[10] Hörmander, L.:L 2 estimates and existence theorems for the 318-4-operator. Acta Math.113, 89-152 (1965). · Zbl 0158.11002
[11] ?? An introduction to complex analysis in several variables. Princeton, N. J.: Von Norstrand 1966. · Zbl 0138.06203
[12] ?? Wermer, J.: Uniform approximation on compact subsets in 318-5. Math. Scand.23, 5-21 (1968). · Zbl 0181.36201
[13] Kerzman, N.: Hölder andL p estimates for solutions of 318-6u=f in strongly pseudoconvex domains. Comm. Pure Appl. Math.,24, 301-379 (1971). · Zbl 0217.13202
[14] Malgrange, B.: Ideals of differentiable functions. Oxford University Press. 1966. · Zbl 0177.17902
[15] Martineau, A.: ?Sur les fonctionelles analytiques et la transformation de Fourier-Borel?, J. Analyse Math.11, 1-164 (1963). · Zbl 0124.31804
[16] Nirenberg, R., Wells, R. O., Jr.: Approximation theorems on differentiable submanifolds of a complex manifold. Trans. Amer. Soc.142, 15-35 (1969). · Zbl 0188.39103
[17] Ramirez de Arellano, E.: Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis. Math. Ann.184, 172-187 (1970). · Zbl 0189.09702
[18] Sato, M.: Theory of hyperfunctions II. J. Fac. Sci. Univ. Tokyo, Sect. I,8, 387-437 (1960). · Zbl 0097.31404
[19] Schapira, P.: Theorie des Hyperfonctions, Lecture Notes in Mathematics, Vol. 126, Berlin-Heidelberg-New York: Springer 1970 · Zbl 0192.47305
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.