Uniform algebras and approximation on manifolds
Artikel i vetenskaplig tidskrift, 2012

Let Ω⊂Cn be a bounded domain and let A⊂C(Ω¯) be a uniform algebra generated by a set F of holomorphic and pluriharmonic functions. Under natural assumptions on Ω and F we show that the only obstruction to A=C(Ω¯) is that there is a holomorphic disk D⊂Ω¯ such that all functions in F are holomorphic on D, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk.

Författare

Håkan Samuelsson Kalm

Erlend Fornaess Wold

Inventiones Mathematicae

0020-9910 (ISSN) 1432-1297 (eISSN)

Vol. 188 505-523

Ämneskategorier

Matematik

Geometri

Matematisk analys

DOI

10.1007/s00222-011-0351-6