The Cauchy-Riemann equations in infinite dimensions
Journées équations aux dérivées partielles (1998), article no. 8, 8 p.

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

@article{JEDP_1998____A8_0,
     author = {Lempert, L\'aszl\'o},
     title = {The {Cauchy-Riemann} equations in infinite dimensions},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {8},
     pages = {1--8},
     publisher = {Universit\'e de Nantes},
     year = {1998},
     mrnumber = {99k:46081},
     zbl = {01808717},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1998____A8_0/}
}
TY  - JOUR
AU  - Lempert, László
TI  - The Cauchy-Riemann equations in infinite dimensions
JO  - Journées équations aux dérivées partielles
PY  - 1998
SP  - 1
EP  - 8
PB  - Université de Nantes
UR  - http://www.numdam.org/item/JEDP_1998____A8_0/
LA  - en
ID  - JEDP_1998____A8_0
ER  - 
%0 Journal Article
%A Lempert, László
%T The Cauchy-Riemann equations in infinite dimensions
%J Journées équations aux dérivées partielles
%D 1998
%P 1-8
%I Université de Nantes
%U http://www.numdam.org/item/JEDP_1998____A8_0/
%G en
%F JEDP_1998____A8_0
Lempert, László. The Cauchy-Riemann equations in infinite dimensions. Journées équations aux dérivées partielles (1998), article  no. 8, 8 p. http://www.numdam.org/item/JEDP_1998____A8_0/

[C] G. Coeuré Les équations de Cauchy-Riemann sur un espace de Hilbert manuscript

[D] S. Dineen Complex Analysis in Locally Convex Spaces North Holland Amsterdam 1981 | Zbl

[H] C. T. Henrich The ∂ equation with polynominal growth on a Hilbert space Duke Math. J. 40 1973 279-306 | MR | Zbl

[Hö] L. Hörmander An Introduction to Complex Analysis in Several Variables 3rd edition North Holland Amsterdam 1990 | Zbl

[L1] L. Lempert The Dolbeault complex in infinite dimensions I J. Amer. Math. Soc., to appear | Zbl

[L2] L. Lempert The Dolbeault complex in infinite dimensions II manuscript

[L3] L. Lempert The Dolbeault complex in infinite dimensions III in preparation

[L4] L. Lempert Approximation de fonctions holomorphes d'un nombre infini de variables manuscript

[M] P. Mazet Analytic Sets in Locally Convex Spaces North Holland Amsterdam 1984

[NN] A. Newlander, L. Nirenberg Complex analytic coordinates in almost complex manifolds Ann. of Math. 65 1957 391-404 | MR | Zbl

[R] P. Raboin Le problème du ∂ sur un espace de Hilbert Bull. Soc. Math. Fr. 107 1979 225-240 | Numdam | MR | Zbl