Approximation by holomorphic functions on certain product sets in Cⁿ

Barnet Mordecai Weinstock

Vol. 43 (1972), No. 3, 811–822

DOI: 10.2140/pjm.1972.43.811

Abstract

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

Milestones

Received: 22 September 1971

Revised: 3 February 1972

Published: 1 December 1972