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.

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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