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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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The Dolbeault complex in infinite dimensions II
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by László Lempert
J. Amer. Math. Soc. 12 (1999), 775-793
DOI: https://doi.org/10.1090/S0894-0347-99-00296-9
Published electronically: April 13, 1999
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Part I: J. Amer. Math. Soc. (1998), 485-520

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
  • G. Coeuré, Les équations de Cauchy–Riemann sur un espace de Hilbert, manuscript.
  • Robert Deville, Gilles Godefroy, and Václav Zizler, Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 64, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. MR 1211634
  • Seán Dineen, Complex analysis in locally convex spaces, Notas de Matemática [Mathematical Notes], vol. 83, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640093
  • Hans Grauert and Ingo Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\bar \partial f=\alpha$ im Bereich der beschränkten Formen, Rice Univ. Stud. 56 (1970), no. 2, 29–50 (1971) (German). MR 273057
  • G. M. Henkin, Integral representation of functions in strongly pseudoconvex regions, and applications to the $\overline \partial$-problem, Mat. Sb. (N.S.) 82 (124) (1970), 300–308 (Russian). MR 0265625
  • Lars Hörmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR 1045639
  • Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
  • L. Lempert, The Dolbeault complex in infinite dimensions I, J. Amer. Math. Soc. 11 (1998), 485–520.
  • Pierre Mazet, Analytic sets in locally convex spaces, North-Holland Mathematics Studies, vol. 89, North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática [Mathematical Notes], 93. MR 756238
  • Pierre Raboin, Le problème du $\bar \partial$ sur un espace de Hilbert, Bull. Soc. Math. France 107 (1979), no. 3, 225–240 (French, with English summary). MR 544520, DOI 10.24033/bsmf.1893
  • Raymond A. Ryan, Holomorphic mappings on $l_1$, Trans. Amer. Math. Soc. 302 (1987), no. 2, 797–811. MR 891648, DOI 10.1090/S0002-9947-1987-0891648-7
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Bibliographic Information
  • László Lempert
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907–1395
  • MR Author ID: 112435
  • Email: lempert@math.purdue.edu
  • Received by editor(s): September 22, 1998
  • Published electronically: April 13, 1999
  • Additional Notes: This research was partially supported by an NSF grant.
  • © Copyright 1999 American Mathematical Society
  • 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
  • MathSciNet review: 1665984