Components of zero sets of analytic functions in C² in the unit ball or polydisc

Bert Alan Taylor

Vol. 59 (1975), No. 1, 253–265

DOI: 10.2140/pjm.1975.59.253

Abstract

Let Ω denote either the unit ball or unit polydisc in C². Let f be a function analytic on a neighborhood of the closure of Ω, and let V be an irreducible component of {f = 0}∩ Ω. Then there is a bounded analytic function on Ω whose zero set is V .

Mathematical Subject Classification 2000

Primary: 32A10

Milestones

Received: 28 March 1975

Published: 1 July 1975