Abstract
Normality and error formulae for simultaneous rational approximants will be discussed. Simultaneous rational approximants generalize Padé approximants 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 defined by m positive Borel measures supported on the real line. Up to now only two types of systems of Markov functions are known for which more than trivial results can be proved. These are the Angelesco and the Nikishin systems. The present paper concentrates on Nikishin systems. For them, new results about normality, and new error formulae are reviewed, and the proofs sketched.
Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4–2).
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Driver, K., Stahl, H. (1994). Normality and Error Formulae for Simultaneous Rational Approximants to Nikishin Systems. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_9
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DOI: https://doi.org/10.1007/978-94-011-0970-3_9
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