Vol. 43, No. 3, 1972

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Approximation by holomorphic functions on certain product sets in Cn

Barnet Mordecai Weinstock

Vol. 43 (1972), No. 3, 811–822

In this paper we prove several theorems concerning approximation by holomorphic functions on product sets in Cn where each factor is either a compact plane set or the closure of a strongly pseudoconvex domain. In particular we show that every continuous function which is locally approximable by holomorphic functions on such a set is globally approximable. Our results depend on a generalization of a theorem of Andreotti and Stoll on bounded solutions of the inhomogeneous Cauchy-Riemann equations on certain product domains.

Mathematical Subject Classification 2000
Primary: 32E25
Secondary: 46J15
Received: 22 September 1971
Revised: 3 February 1972
Published: 1 December 1972
Barnet Mordecai Weinstock