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Titlebook: Nonlinear Numerical Methods and Rational Approximation II; Annie Cuyt Book 1994 Springer Science+Business Media Dordrecht 1994 Meromorphic

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Orthogonality and Boundary Interpolation quasi-definite linear functional on., and define the inner product., where .. (In particular . may be a positive definite functional given by.,where µ is a measure such that all functions in . are µ-integrable).Let .be an orthogonal system obtained from the basis . by the Gram-Sdunidt method and de
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Gegenbauer-Sobolev Orthogonal Polynomialsmials algebraic and differential properties are obtained, as well as the relation with the classical Gegenbauer polynomials Finally, some properties concerning the localization and separation of the zeros of these polynomials are deduced.
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Inverse Problems: Rational Modificationsequation . for α ∈ – {0} If we fix a solution . we obtain the corresponding sequence of moments, characterize the regularity and we determine the expression for the sequence of monic orthogonal polynomials related to .. Finally we study the positive definite case, we obtain the relation between the
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Normality and Error Formulae for Simultaneous Rational Approximants to Nikishin Systems and continued fractions in a very natural way. As in the case of Padé approximants so also here Markov functions are especially interesting and important. The common denominator of the simultaneous approximants satisfies a multiple orthogonality relation, which in the case of Markov functions is de
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