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Strong Asymptotics for Extremal Polynomials Associated with Weights on R
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ISBN
:
9783540189589
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Publisher
:
Springer
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Subject
:
Mathematics
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Binding
:
Paperback
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Pages
:
160
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Year
:
415
₹
2344.0
₹
2344.0
2344.0
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Description
The aim of this research monograph is to establish strong, or SzegA type asymptotics for extremal polynomials associated with weights W(x): = exp (-Q(x)) on . While the Q(x) treated are fairly general - even and of smooth polynomial growth at infinity - a typical example is Q(x): =, > 0. The results are consequences of a strengthened form of the following assertion: Given 0 , f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 0 for a.e. ">" 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.0. The results are consequences of a strengthened form of the following assertion: Given 0 , f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 0 for a.e. ">" 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.
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