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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A unified approach to uniform real approximation by polynomials with linear restrictions

Author: Bruce L. Chalmers
Journal: Trans. Amer. Math. Soc. 166 (1972), 309-316
MSC: Primary 41A50
MathSciNet review: 0294962
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Abstract: Problems concerning approximation of real-valued continuous functions of a real variable by polynomials of degree smaller than n with various linear restrictions have been studied by several authors. This paper is an attempt to provide a unified approach to these problems. In particular, the notion of restricted derivatives approximation is seen to fit into the theory and includes as special cases the notions of monotone approximation and restricted range approximation. Also bounded coefficients approximation, $\varepsilon$-interpolator approximation, and polynomial approximation with interpolation fit into our scheme.

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Keywords: Approximation with linear restrictions, polynomials of best approximation, extremal sets, uniqueness of best approximation, generalized Haar condition
Article copyright: © Copyright 1972 American Mathematical Society