Vladimir V. Andrievskii, Hans-Peter Blatt

Broschiertes Buch

Discrepancy of Signed Measures and Polynomial Approximation

Beschreibung

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 fbe 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.

Produktdetails

• Springer Monographs in Mathematics
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-3146-7
• Softcover reprint of hardcover 1st ed. 2002
• Seitenzahl: 456
• Erscheinungstermin: 6. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 25mm
• Gewicht: 686g
• ISBN-13: 9781441931467
• ISBN-10: 1441931465
• Artikelnr.: 32221360