Limit Theorems of Polynomial Approximation with Exponential Weights
Author： Michael I. Ganzburg
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405038
P-ISBN(Paperback): 9780821840634
P-ISBN(Hardback): 9780821840634
Subject： O174.5 complex - variable function
Keyword： Analysis
Language： ENG
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Limit Theorems of Polynomial Approximation with Exponential Weights
Description
The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation. In addition he establishes new inequalities for polynomials in complex domains and new asymptotics and estimates for orthogonal polynomials with exponential weights. More detailed information on approximation properties of functions is obtained for the canonical weights $W(x)=\exp(-|x|^\alpha),\, 0<\alpha<\infty$, and some other weights.