Discrepancy of Signed Measures and Polynomial Approximation (Springer Monographs in Mathematics) - Hardcover

Andrievskii, Vladimir V.; Blatt, Hans-Peter

Hardcover

ISBN 10: 0387986529 ISBN 13: 9780387986524

Publisher: Springer, 2001

Synopsis

A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.

About this title

From the Back Cover

The book is an authoritative and up-to-date introduction to the field of Analysis and Potential Theory dealing with the distribution zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compact sets and on the real line. The main feature of the book is the combination of potential theory with conformal invariants, such as module of a family of curves and harmonic measure, to derive discrepancy estimates for signed measures if bounds for their logarithmic potentials or energy integrals are known a priori. Classical results of Jentzsch and Szegö for the zero distribution of partial sums of power series can be recovered and sharpened by new discrepany estimates, as well as distribution results of Erdös and Turn for zeros of polynomials bounded on compact sets in the complex plane.
Vladimir V. Andrievskii is Assistant Professor of Mathematics at Kent State University. Hans-Peter Blatt is Full Professor of Mathematics at Katholische Universität Eichstätt.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0387986529
• ISBN 13: 9780387986524
• Binding: Hardcover
• Number of pages: 452