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1. CJM 2006 (vol 58 pp. 249)

Bello Hernández, M.; Mínguez Ceniceros, J.
 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 problemCategories:41A20, 41A21, 44A60

2. CJM 1997 (vol 49 pp. 1034)

Saff, E. B.; Stahl, H.
 Ray sequences of best rational approximants for $|x|^\alpha$ The convergence behavior of best uniform rational approximations $r^\ast_{mn}$ with numerator degree~$m$ and denominator degree~$n$ to the function $|x|^\alpha$, $\alpha>0$, on $[-1,1]$ is investigated. It is assumed that the indices $(m,n)$ progress along a ray sequence in the lower triangle of the Walsh table, {\it i.e.} the sequence of indices $\{ (m,n)\}$ satisfies $${m\over n}\rightarrow c\in [1, \infty)\quad\hbox{as } m+ n\rightarrow\infty.$$ In addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function $|x|^\alpha - r^\ast_{mn} (x)$ on $[-1,1]$ will be studied. The results will be compared with those for paradiagonal sequences $(m=n+2[\alpha/2])$ and for sequences of best polynomial approximants. Keywords:Walsh table, rational approximation, best approximation,, distribution of poles and zeros.Categories:41A25, 41A44