Strong Asymptotics for Extremal Polynomials Associated with Weights on R: 1305 - Brossura

Lubinsky, Doron S.

Brossura

ISBN 10: 3540189580 ISBN 13: 9783540189589

Casa editrice: Springer Berlin Heidelberg, 2010

Riassunto

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.

Su questo libro

Contenuti

Notation and index of notation.- Statement of main results.- Weighted polynomials and zeros of extremal polynomials.- Integral equations.- Polynomial approximation of potentials.- Infinite-finite range inequalities and their sharpness.- The largest zeros of extremal polynomials.- Further properties of Un, R(x).- Nth root asymptotics for extremal polynomials.- Approximation by certain weighted polynomials, I.- Approximation by certain weighted polynomials, II.- Bernstein's formula and bernstein extremal polynomials.- Proof of the asymptotics for Enp(W).- Proof of the asymptotics for the Lp extremal polynomials.- The case p=2 : Orthonormal polynomials.

Dettagli dell'edizione

• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3540189580
• ISBN 13: 9783540189589
• Rilegatura: Copertina flessibile
• Numero di pagine: 168
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania