Discrepancy of Signed Measures and Polynomial Approximation - Andrievskii, Vladimir V.; Blatt, Hans-Peter
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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.

Produktbeschreibung
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.
  • Produktdetails
  • Springer Monographs in Mathematics
  • Verlag: Springer, Berlin
  • Softcover reprint of hardcover 1st ed. 2002
  • Seitenzahl: 456
  • Erscheinungstermin: 6. Dezember 2010
  • Englisch
  • Abmessung: 235mm x 155mm x 24mm
  • Gewicht: 686g
  • ISBN-13: 9781441931467
  • ISBN-10: 1441931465
  • Artikelnr.: 32221360
Autorenporträt
Analysis is the branch of mathematics concerned with limits of functions, sequences and series. Potential theory is the study of potential functions. This book is an authoritative and up-to-date introduction to both fields.
Inhaltsangabe
Preface 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
Rezensionen
From the reviews of the first edition: "Distributions of certain point sets are in many respects important in approximation theory. ... Many classical theorems ... deal with such problems. This book collects a number of generalizations of these theorems. ... The book is written with great care. ... This monograph is a valuable addition to the library of any researcher in approximation theory. The topic is rather specialized, but the style and the importance of potential theory in the discipline, makes it also suited for an advanced course in approximation theory." (Simon Stevin Bulletin, Vol. 11 (1), 2004) "This book is devoted to discrepancy estimates for the zero of polynomials and for signed measures. ... A remarkable feature of the book is that most of the results in it are shown to be sharp. ... This work is a valuable monograph on a field that has attracted considerable interest in the recent past, and which has various applications in approximation theory and orthogonal polynomials." (Vilmos Totik, Bulletin of the London Mathematical Society, Vol. 35, 2003) "This book discusses in detail the discrepancy of signed measures ... . The detailed proofs and the rich reference make this book eligible for a self-study textbook and a reference book, too." (Béla Nagy, Acta Scientiarum Mathematicarum, Vol. 68, 2002)