Logarithmic potentials with external fields
By: Edward B. Saff, Vilmos Totik.
Contributors: Totik, V.
Series: Grundlehren der mathematischen Wissenschaften,; 316
Publisher: Springer
Published: 1997
Place of publication: Berlin; New York
Language: eng
Number of pages: 505
Subjects: Potential theory (Mathematics)
Description: This treatment of potential theory emphasizes the effects of an external field (or weight) on the minimum energy problem. Several important aspects of the external field problem (and its extension to signed measures) justify its special attention. The most striking is that it provides a unified approach to seemingly different problems in constructive analysis. These include the asymptotic analysis of orthogonal polynomials, the limited behavior of weighted Fekete points; the existence and construction of fast decreasing polynomials; the numerical conformal mapping of simply and doubly connected domains; generalization of the Weierstrass approximation theorem to varying weights; and the determination of convergence rates for best approximating rational functions.
Notes: Includes bibliographical references (p. [485]-494) and index.