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Aproximaciones asintóticas en espacios de Banach.

Piedad Guijarro Carranza (1985)

Stochastica

Let U be an open convex set in a Banach space E, F another Banach space. We consider the space HUb(U,F) of all F-valued holomorphic functions of bounded type in U possesing an asymptotic expansion in the origin. We study classes of asymptotic approximations such that two functions in the same class with an identical asymptotic expansion must coincide. In this paper, we characterize the functions belonging to some of these classes which are optimal approximations of a given series.

Asymptotic distribution of poles and zeros of best rational approximants to x α on [0,1]

E. Saff, H. Stahl (1995)

Banach Center Publications

Let r n * ∈ ℛ n n be the best rational approximant to f ( x ) = x α , 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of r n * lie on the negative axis ℝ < 0 . In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function e n = f - r n * on [0,1], and survey related convergence results.

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