Geodesic
Convergence of Interpolation to Transforms of Totally Positive Kernels
Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 750-768

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Dyn, N.; Lubinsky, D. S. Convergence of Interpolation to Transforms of Totally Positive Kernels. Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 750-768. doi: 10.4153/CJM-1988-033-9
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