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Convergence of Interpolation to Transforms of Totally Positive Kernels

Published online by Cambridge University Press:  20 November 2018

N. Dyn  and
D. S. Lubinsky
N. Dyn
Affiliation:
Tel Aviv University, Tel Aviv, Israel
D. S. Lubinsky
Affiliation:
Centre for Advanced Computing and Decision Support, Pretoria, Republic of South Africa
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Convergence of exponential sums

that interpolate to Laplace transforms

(1.1)

have been studied by several authors [3, 6, 8, 15]. For rational functions that interpolate to Markov functions (also called Hamburger or Stieltjes Series or Hilbert Transforms)

(1.2)

far more detailed convergence results are available (see [10, 11, 16] and references therein). Both (1.1) and (1.2) are special cases of the transform

(1.3)

where K(x, t) is a strictly totally positive kernel.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 3 , 01 June 1988 , pp. 750 - 768
Copyright
Copyright © Canadian Mathematical Society 1988

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