1. CJM 2007 (vol 59 pp. 3)
|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)
|Convergence of Fourier--PadÃ© 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 PadÃ© approximants, Fourier--PadÃ© approximants, moment problem
Categories:41A20, 41A21, 44A60