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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0294962-0
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0294962-0
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

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