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The Dolbeault complex in infinite dimensions II


Author: László Lempert
Journal: J. Amer. Math. Soc. 12 (1999), 775-793
MSC (1991): Primary 32F20, 46G20
DOI: https://doi.org/10.1090/S0894-0347-99-00296-9
Published electronically: April 13, 1999
Part I: J. Amer. Math. Soc. (1998), 485-520
MathSciNet review: 1665984
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the equation $\overline{\partial }u=f$ on a ball $B(R)\subset l^{1}$, and prove that it is solvable if $f$ is a Lipschitz continuous, closed $(0,1)$-form.


References [Enhancements On Off] (What's this?)

  • [C] G. Coeuré, Les équations de Cauchy-Riemann sur un espace de Hilbert, manuscript.
  • [DGZ] R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces, Longman Scientific & Technical, Essex, England, 1993. MR 94d:46012
  • [D] S. Dineen, Complex Analysis in Locally Convex Spaces, North Holland, Amsterdam, 1981. MR 84b:46050
  • [GL] H. Grauert, I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\overline{\partial}f=\alpha $ im Bereiche der beschränkten Formen, Proc. Conf. Complex Analysis, 1969, Rice University, Rice University Studies 56 (1970), 29-50. MR 42:7938
  • [H] G.M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb. 82 (1970), 300-308; English translation, Math. USSR Sb. 11 (1970), 273-281. MR 42:534
  • [Ho] L. Hörmander, An Introduction to Complex Analysis in Several Variables, 3rd edition, North Holland, Amsterdam, 1990. MR 91a:32001
  • [K] J. Kurzweil, On approximations in real Banach spaces, Studia Math. 14 (1954), 214-231. MR 16:932g
  • [L] L. Lempert, The Dolbeault complex in infinite dimensions I, J. Amer. Math. Soc. 11 (1998), 485-520. CMP 98:13
  • [M] P. Mazet, Analytic Sets in Locally Convex Spaces, North Holland, Amsterdam, 1984. MR 86i:32012
  • [R] P. Raboin, Le problème du $\overline{\partial}$ sur un espace de Hilbert, Bull. Soc. Math. Fr. 107 (1979), 225-240. MR 80i:32052
  • [Ry] R.A. Ryan, Holomorphic mappings in $l^{1}$, Trans. Amer. Math. Soc. 302 (1987), 797-811. MR 88h:46089

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Additional Information

László Lempert
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907–1395
Email: lempert@math.purdue.edu

DOI: https://doi.org/10.1090/S0894-0347-99-00296-9
Keywords: $\overline{\partial }$ equation, Banach spaces
Received by editor(s): September 22, 1998
Published electronically: April 13, 1999
Additional Notes: This research was partially supported by an NSF grant.
Article copyright: © Copyright 1999 American Mathematical Society

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