Abstract
In recent years, certain aspects of the theory of best polynomial approximation on a real interval have been generalized. Classical theorems concerning existence and uniqueness of a polynomial of best approximation, and characterization of this polynomial by alternation properties, have found extensions and analogs when polynomials are replaced by linear combinations of prescribed continous functions. See, e.g. [2, 3, 4, 5, 7, 8, 9, 10, 11], for typical studies of this kind (especially [8], [11] for the general background). Quite recently, there has been some interest ([1], [6]) in corresponding extensions of the theory of approximation by rational functions. The present note is a contribution to this discussion.
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Newman, D.J., Shapiro, H.S. (1964). Approximation by Generalized Rational Functions. In: Butzer, P.L., Korevaar, J. (eds) On Approximation Theory / Über Approximationstheorie. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Nummerischen Mathematik / Série Internationale D’Analyse Numérique, vol 5 . Springer, Basel. https://doi.org/10.1007/978-3-0348-4131-3_25
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