Discrepancy of Signed Measures and Polynomial Approximation

Language: English

Published by Springer US, 2001

0387986529 / 9780387986524

Series: Book 15 of 187 - Springer Monographs in Mathematics

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Druck auf Anfrage Neuware - Printed after ordering - In many situations in approximation theory the distribution of points in a given set is of interest. For example, the suitable choiee of interpolation points is essential to obtain satisfactory estimates for the convergence of interpolating polynomials. Zeros of orthogonal polynomials are the nodes for Gauss quadrat ure formulas. Alternation points of the error curve char acterize the best approximating polynomials. In classieal complex analysis an interesting feature is the location of zeros of approximants to an analytie function. In 1918 R. Jentzsch [91] showed that every point of the circle of convergence of apower series is a limit point of zeros of its partial sums. This theorem of Jentzsch was sharpened by Szegö [170] in 1923. He proved that for apower series with finite radius of convergence there is an infinite sequence of partial sums, the zeros of whieh are 'equidistributed' with respect to the angular measure. In 1929 Bernstein [27] stated the following theorem. Let f be a positive continuous function on [-1, 1]; if almost all zeros of the polynomials of best 2 approximation to f (in a weighted L -norm) are outside of an open ellipse c with foci at -1 and 1, then f has a continuous extension that is analytic in c.…

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Title
Discrepancy of Signed Measures and Polynomial Approximation
Author
Hans-Peter Blatt
Publisher
Springer US
Publication year
2001
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0387986529
ISBN 13
9780387986524
Item weight
800 grams
Dimensions
241x160x30 mm
Series
Book 15 of 187: Springer Monographs in Mathematics

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