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Search: MSC category 32E30 ( Holomorphic and polynomial approximation, Runge pairs, interpolation )

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1. CJM 2007 (vol 59 pp. 3)

Biller, Harald
Holomorphic Generation of Continuous Inverse Algebras
We study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixed $n$-tuple of elements are dense. In particular, we characterize the compact subsets of~$\C^n$ which appear as joint spectra of such $n$-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.

Keywords:holomorphic functional calculus, commutative continuous inverse algebra, holomorphic convexity, Stein compacta, meromorphic convexity, holomorphic approximation
Categories:46H30, 32A38, 32E30, 41A20, 46J15

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