On weighted polynomial approximation with monotone weights
نویسندگان
چکیده
منابع مشابه
A Survey of Weighted Polynomial Approximation with Exponential Weights
Let W : R → (0, 1] be continuous. Bernstein’s approximation problem, posed in 1924, deals with approximation by polynomials in the weighted uniform norm f → ‖fW‖L∞(R). The qualitative form of this problem was solved by Achieser, Mergelyan, and Pollard, in the 1950’s. Quantitative forms of the problem were actively investigated starting from the 1960’s. We survey old and recent aspects of this t...
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We prove here some polynomial approximation theorems, somewhat related to the Szasz-Mfintz theorem, but where the domain of approximation is the integers, by dualizing a gap theorem of C. l ~ Y I for periodic entire functions. In another Paper [7], we shall prove, by similar means, a completeness theorem ibr some special sets of entire functions. I t is well known (see, for example [l]) tha t i...
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We prove that if f is increasing on [ 1,1], then for each n = 1, 2 . . . . . there is an increasing algebraic polynomial P. of degree n such that {f(x) P.(x){ < cw2( f, V/I x 2 /n) , where w2 is the second-order modulus of smoothness. These results complement the classical pointwise estimates of the same type for unconstrained polynomial approximation. Using these results, we characterize the m...
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Given a pair (G,W ) of an open bounded set G in the complex plane and a weight function W (z) which is analytic and different from zero in G, we consider the problem of the locally uniform approximation of any function f(z), which is analytic in G, by weighted polynomials of the form {Wn(z)Pn(z)}n=0, where deg Pn ≤ n. The main result of this paper is a necessary and sufficient condition for suc...
متن کاملThe generalized Bernstein problem on weighted Lacunary polynomial approximation
We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted Lp spaces of functions on the real line. This generalizes the solution to the classical Bernstein problem given by Izumi, Kawata and Hall. © 2005 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05511-8