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Search: MSC category 41A20 ( Approximation by rational functions )

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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

2. CJM 2006 (vol 58 pp. 249)

Bello Hernández, M.; Mínguez Ceniceros, J.
Convergence of Fourier--Padé Approximants for Stieltjes Functions
We prove convergence of diagonal multipoint Pad\'e approximants of Stieltjes-type functions when a certain moment problem is determinate. This is used for the study of the convergence of Fourier--Pad\'e and nonlinear Fourier--Pad\'e approximants for such type of functions.

Keywords:rational approximation, multipoint Padé approximants, Fourier--Padé approximants, moment problem
Categories:41A20, 41A21, 44A60

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