Duke Mathematical Journal

A critical growth rate for the pluricomplex Green function

Siegfried Momm

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Article information

Duke Math. J. Volume 72, Number 2 (1993), 487-502.

First available in Project Euclid: 20 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32F05
Secondary: 32A15: Entire functions 35R50: Partial differential equations of infinite order


Momm, Siegfried. A critical growth rate for the pluricomplex Green function. Duke Math. J. 72 (1993), no. 2, 487--502. doi:10.1215/S0012-7094-93-07218-3. http://projecteuclid.org/euclid.dmj/1077289429.

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  • [1] L. Ehrenpreis, Solution of some problems of division. IV. Invertible and elliptic operators, Amer. J. Math. 82 (1960), 522–588.
  • [2] L. Hörmander, On the range of convolution operators, Ann. of Math. (2) 76 (1962), 148–170.
  • [3] L. Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966.
  • [4] M. Klimek, Pluripotential theory, London Mathematical Society Monographs. New Series, vol. 6, The Clarendon Press Oxford University Press, New York, 1991.
  • [5] A. S. Krivosheev, A criterion for the solvability of nonhomogeneous convolution equations in convex domains of $\mathbbC^N$, Math. USSR-Izv. 36 (1991), 497–517.
  • [6] M. Langenbruch, Splitting of the $\overline\partial$-complex in weighted spaces of square integrable functions, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 2-3, 201–223.
  • [7] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), no. 4, 427–474.
  • [8] B. J. Levin, Distribution of Zeros of Entire Functions, Transl. Math. Monographs, vol. 5, American Mathematical Society, Providence, R.I., 1964.
  • [9] A. Martineau, Équations différentielles d'ordre infini, Bull. Soc. Math. France 95 (1967), 109–154.
  • [10] R. Meise and B. A. Taylor, Splitting of closed ideals in $(\rm DFN)$-algebras of entire functions and the property $(\rm DN)$, Trans. Amer. Math. Soc. 302 (1987), no. 1, 341–370.
  • [11] R. Meise and B. A. Taylor, Each nonzero convolution operator on the entire functions admits a continuous linear right inverse, Math. Z. 197 (1988), no. 1, 139–152.
  • [12] R. Meise and D. Vogt, Einführung in die Funktionalanalysis, Vieweg Studium: Aufbaukurs Mathematik [Vieweg Studies: Mathematics Course], vol. 62, Friedr. Vieweg & Sohn, Braunschweig, 1992.
  • [13] S. Momm, Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc, Studia Math. 96 (1990), no. 1, 51–71.
  • [14] S. Momm, Convex univalent functions and continuous linear right inverses, J. Funct. Anal. 103 (1992), no. 1, 85–103.
  • [15] S. Momm, A division problem in the space of entire functions of exponential type, to appear in Ark. Mat.
  • [16] S. Momm, Division problems in spaces of entire functions of finite order, to appear in Functional Analysis, ed. by Bierstedt, Pietsch, Ruess, and Vogt, Marcel Dekker, New York.
  • [17] S. Momm, Boundary behavior of extremal plurisubharmonic functions, preprint.
  • [18] V. V. Morzhakov, On epimorphicity of a convolution operator in convex domains in $\mathbbC^N$, Math. USSR-Sb. 60 (1988), 347–364.
  • [19] R. T. Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970.
  • [20] W. Rudin, Real and complex analysis, Third edition ed., McGraw-Hill Book Co., New York, 1987.
  • [21] K. Schwerdtfeger, Faltungsoperatoren auf Räumen holomorpher und beliebig oft differenzierbarer Funktionen, thesis, Düsseldorf, 1982.
  • [22] J. Siciak, Extremal plurisubharmonic functions in $\bf C\spn$, Ann. Polon. Math. 39 (1981), 175–211.
  • [23] R. Sigursson, Convolution equations in domains of $\bf C\sp n$, Ark. Mat. 29 (1991), no. 2, 285–305.
  • [24] B. A. Taylor, Linear extension operators for entire functions, Michigan Math. J. 29 (1982), no. 2, 185–197.
  • [25] F. Tréves, Linear partial differential equations with constant coefficients: Existence, approximation and regularity of solutions, Mathematics and its Applications, vol. 6, Gordon and Breach Science Publishers, New York, 1966.