Discrepancy of Signed Measures and Polynomial Approximation

Vladimir V. Andrievskii, Hans-Peter Blatt

438 pages, parution le 17/01/2002

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Résumé

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.

Sommaire

Auxiliary Facts.
Zero Distribution of Polynomials.
Discrepancy Theorems via Two
Sided Bounds for Potentials.
Discrepancy Thoerems via One
Sided Bounds for Potentials.
Discrepancy Theorems via Energy Integrals.
Applications of Jentzsch
Szegö and Erdös
Turán Type Theorems.
Applications of Discrepancy Theorems.
Special Topics.
Appendix A: Conformally Invariant Characteristics of Curve Families.
Appendix B: Basics in the Theory of Quasiconformal Mappings.
Appendix C: Constructive Theory of Functions of a Complex Variable.
Appendix D: Miscellaneous Topics.
Bibliography.
Glossary of Notation.
Index.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Vladimir V. Andrievskii, Hans-Peter Blatt
Parution	17/01/2002
Nb. de pages	438
Format	16 x 24
Couverture	Relié
Poids	700g
Intérieur	Noir et Blanc
EAN13	9780387986524
ISBN13	978-0-387-98652-4