Abstract
In this paper we establish the general inequalities for diagonal and subdiagonal multipoint Pade approximants to a Stieltjes function f in terms of power expansion of f on the real line. The inequalities derived produce the best upper and lower bounds on f with respect to the given coefficients of Stieltjes series. As an example of applications sequences of upper and lower Pade bounds converging to the effective dielectric constant of a random array of spheres are evaluated. Mathematics subject classification (2010): 11J70, 41A21.
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