The Cauchy-Riemann equations in infinite dimensions

László Lempert

Journées équations aux dérivées partielles (1998)

  • page 1-8
  • ISSN: 0752-0360

Abstract

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I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.

How to cite

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Lempert, László. "The Cauchy-Riemann equations in infinite dimensions." Journées équations aux dérivées partielles (1998): 1-8. <http://eudml.org/doc/93365>.

@article{Lempert1998,
abstract = {I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.},
author = {Lempert, László},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-8},
publisher = {Université de Nantes},
title = {The Cauchy-Riemann equations in infinite dimensions},
url = {http://eudml.org/doc/93365},
year = {1998},
}

TY - JOUR
AU - Lempert, László
TI - The Cauchy-Riemann equations in infinite dimensions
JO - Journées équations aux dérivées partielles
PY - 1998
PB - Université de Nantes
SP - 1
EP - 8
AB - I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.
LA - eng
UR - http://eudml.org/doc/93365
ER -

References

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  1. [C] G. CoeuréLes équations de Cauchy-Riemann sur un espace de Hilbert manuscript 
  2. [D] S. DineenComplex Analysis in Locally Convex Spaces North Holland Amsterdam1981 Zbl0484.46044
  3. [H] C. T. HenrichThe ∂ equation with polynominal growth on a Hilbert space Duke Math. J. 40 1973 279-306 Zbl0261.35063MR47 #9279
  4. [Hö] L. HörmanderAn Introduction to Complex Analysis in Several Variables 3rd edition North Holland Amsterdam 1990 Zbl0685.32001
  5. [L1] L. LempertThe Dolbeault complex in infinite dimensions I J. Amer. Math. Soc., to appear Zbl0904.32014
  6. [L2] L. LempertThe Dolbeault complex in infinite dimensions II manuscript 
  7. [L3] L. LempertThe Dolbeault complex in infinite dimensions III in preparation 
  8. [L4] L. LempertApproximation de fonctions holomorphes d'un nombre infini de variables manuscript 
  9. [M] P. MazetAnalytic Sets in Locally Convex Spaces North Holland Amsterdam1984 
  10. [NN] A. Newlander, L. NirenbergComplex analytic coordinates in almost complex manifolds Ann. of Math. 65 1957 391-404 Zbl0079.16102MR19,577a
  11. [R] P. RaboinLe problème du ∂ sur un espace de Hilbert Bull. Soc. Math. Fr. 107 1979 225-240 Zbl0414.46030MR80i:32052

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