Uniform approximation on compact subsets of the real line |
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Authors: | M. B. Korobkova |
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Affiliation: | 1. Leningrad Institute of Electrical Engineering and Communication, USSR
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Abstract: | Let {? i } i=∩ n be continuous real functions on the compact set M?R. We consider the problem of best uniform approximation of the function? by polynomials (sumnolimits_{i = 1}^n {c_i varphi _i }) on M. Let V(?0, A) be a set of polynomials of best approximation on A ? M. We show that (V(varphi _0 ,M) = mathop cap limits_{A_{n + 1} } V(varphi _0 ,A_{n + 1} )) , where An+1 represents all the possible sets of n+ 1 points {x1, ..., xn+1} in M, containing the characteristic set of the given problem of best approximation and for which the the rank of ∥?i ∥ (i=1, ...,n; j=1,..., n+1) is equal to n. This theorem is applied to a problem of uniform approximation where {? i } i=1 n is a weakly Chebyshev system. |
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