Polynomial approximation with doubling weights
نویسندگان
چکیده
منابع مشابه
Polynomial approximation with doubling weights having finitely many zeros and singularities
We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights w having finitely many zeros and singularities (i.e., points where w becomes infinite) on an interval and not too “rapidly changing” away from these zeros and singularities. This class of doubling weights is rather wide and, in particular, includes the classical Jacobi weights, generaliz...
متن کاملMultivariate polynomial inequalities with respect to doubling weights and A∞ weights
In one-dimensional case, various important, weighted polynomial inequalities, such as Bernstein, Marcinkiewicz–Zygmund, Nikolskii, Schur, Remez, etc., have been proved under the doubling condition or the slightly stronger A∞ condition on the weights by Mastroianni and Totik in a recent paper [G. Mastroianni, V. Totik, Weighted polynomial inequalities with doubling and A∞ weights, Constr. Approx...
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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...
متن کاملNotes on Inequalities with Doubling Weights
Various important weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc. inequalities, have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most of the cases this minimal assumption is the doubling condition. Sometimes however, like in the weighted Nikolskii inequality, the slightly stronger A∞...
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It has been known for some years that the uniformdensity problem for forward neural networks has a positive answer: Any real-valued, continuous function on a compact subset of R can be uniformly approximated by a sigmoidal neural network with one hidden layer. We design here algorithms for efficient uniform approximation by a certain class of neural networks with one hidden layer which we call ...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2015
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-015-0519-4