×
Hörmander, Lars

\(L^2\) estimates and existence theorems for the \(\overline\partial\)-operator. (English) Zbl 0158.11002

Acta Math. 113, 89-152 (1965).
Reviewer: James Eells (Cambridge)
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0158.11002

Cited in 6 Reviews
Cited in 525 Documents

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators

Keywords:

partial differential equations

Citations:

Zbl 0090.38401; Zbl 0161.09302; Zbl 0178.11305
PDFBibTeX XMLCite
\textit{L. Hörmander}, Acta Math. 113, 89--152 (1965; Zbl 0158.11002)
Full Text: DOI

References:

[1] Andreotti, A. &Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes.Bull. Soc. Math. France, 90 (1962), 193–259. · Zbl 0106.05501
[2] Ash, M. E., The basic estimate of the \(\bar \partial \) -Neumann problem in the non-Kählerian case.Amer. J. Math., 86 (1964), 247–254. · Zbl 0124.31103 · doi:10.2307/2373162
[3] Bergman, S., Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I–II.J. Reine Angew. Math., 169 (1933), 1–42, and 172 (1935), 89–128. · JFM 59.0030.02 · doi:10.1515/crll.1933.169.1
[4] Bers, L.,Several complex variables. Lecture notes, New York University, 1963.
[5] Bremermann, H., Complex convexity.Trans. Amer. Math. Soc., 82 (1956), 17–51. · Zbl 0070.30402 · doi:10.1090/S0002-9947-1956-0079100-2
[6] –, Über die Äquivalenz der pseudoconvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Veränderlichen.Math. Ann., 128 (1954), 63–91. · Zbl 0056.07801 · doi:10.1007/BF01360125
[7] Cartan, H.,Séminaires E.N.S. 1951/1952.
[8] Ehrenpreis, L., Some applications of the theory of distributions to several complex variables.Seminar on analytic functions I, 65–79. Institute for Advanced Study, Princeton 1957.
[9] Ehrenpreis, L., A fundamental principle for systems of linear differential equations with constant coefficients, and some of its applications.Proc. Intern. Symp. on Linear spaces, Jerusalem 1961, 161–174. · Zbl 0117.33403
[10] Friedrichs, K., The identity of weak and strong extensions of differential operators.Trans. Amer. Math. Soc., 55 (1944), 132–151. · Zbl 0061.26201
[11] Garabedian, P. R. &Spencer, D. C., Complex boundary problems.Trans. Amer. Math. Soc., 73 (1952), 223–242. · Zbl 0049.18101 · doi:10.1090/S0002-9947-1952-0051326-X
[12] Hörmander, L.,Linear partial differential operators. Springer 1963. · Zbl 0108.09301
[13] –, Weak and strong extensions of differential operators.Comm. Pure Appl. Math., 14 (1961), 371–379. · Zbl 0111.29202 · doi:10.1002/cpa.3160140314
[14] Kohn, J. J., Harmonic integrals on strongly pseudo-convex manifolds I.Ann. Math. (2), 78 (1963), 112–148. · Zbl 0161.09302 · doi:10.2307/1970506
[15] –, Regularity at the boundary of the \(\bar \partial \) -Neumann problem.Proc. Nat. Acad. Sci. U.S.A., 49 (1963), 206–213. · Zbl 0118.31101 · doi:10.1073/pnas.49.2.206
[16] –, Harmonic integrals on strongly pseudo-convex manifolds II.Ann. Math. (2), 79 (1964), 450–472. · Zbl 0178.11305 · doi:10.2307/1970404
[17] Lax, P. D. &Phillips, R. S., Local boundary conditions for dissipative symmetric linear differential operators.Comm. Pure Appl. Math. 13 (1960), 427–455. · Zbl 0094.07502 · doi:10.1002/cpa.3160130307
[18] Lelong, P., Les fonctions plurisousharmoniques.Ann. Sci. École Norm. Sup. 62 (1945) 301–338. · Zbl 0061.23205
[19] Malgrange, B.,Lectures on the theory of functions of several complex variables. Tata Institute of Fundamental Research, Bombay 1958.
[20] Malgrange, B., Sur les systèmes differentiels a coefficients constants.Coll. int. du CNRS, Paris 1963. · Zbl 0231.46073
[21] Martineau, A., Sur les fonctionnelles analytiques et la transformation de Fourier-Borel.J. Analyse Math., 9 (1963), 1–164. · Zbl 0124.31804 · doi:10.1007/BF02789982
[22] Morse, A. P., The behavior of a function on its critical set.Ann. Math. (2), 40 (1939), 62–70. · JFM 65.0207.03 · doi:10.2307/1968544
[23] Morrey, C. B., The analytic embedding of abstract real analytic manifolds.Ann. Math. (2), 68 (1958), 159–201. · Zbl 0090.38401 · doi:10.2307/1970048
[24] Nagy, B. v. Sz.,Spektraldarstellung linearer Transformationen des Hilbertschen Raumes. Berlin 1942. · JFM 68.0241.01
[25] Newlander, A. &Nirenberg, L., Complex analytic coordinates in almost complex manifolds.Ann. Math. (2), 65 (1957), 391–404. · Zbl 0079.16102 · doi:10.2307/1970051
[26] Norguet, F., Sur les domaines d’holomorphie des fonctions uniformes de plusieurs variables complexes.Bull. Soc. Math. France, 82 (1954), 137–159. · Zbl 0056.07701
[27] Oka, K., Sur les fonctions analytiques de plusieurs variables. VI. Domaines pseudoconvexes.Tôhuku Math. J., 49 (1942), 19–52. · Zbl 0060.24006
[28] –, Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique interieur.Japan J. Math., 23 (1954), 97–155.
[29] Pólya, G., Untersuchungen über Lücken und Singularitäten von Potenzreihen.Math. Z., 29 (1929), 549–640. · JFM 55.0186.02 · doi:10.1007/BF01180553
[30] Weil, A.,Variétés Kählériennes. Hermann, Paris, 1958.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.