Polynomials and Polynomial Inequalities

1995
ISBN: 978-0-387-94509-5
Verlag: Springer

Buch, Englisch, Band 161, 480 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1920 g

Reihe: Graduate Texts in Mathematics

Polynomials pervade mathematics, virtually every branch of mathematics from algebraic number theory and algebraic geometry to applied analysis and computer science, has a corpus of theory arising from polynomials. The material explored in this book primarily concerns polynomials as they arise in analysis; it focuses on polynomials and rational functions of a single variable. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.
After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality conclude the book.

Zielgruppe

Graduate

Autoren/Hrsg.

Erdelyi, Tamas

Borwein, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Chaptern 1 Introduction and Basic Properties.- 2 Some Special Polynomials.- 3 Chebyshev and Descartes Systems.- 4 Denseness Questions.- 5 Basic Inequalities.- 6 Inequalities in Müntz Spaces.- Inequalities for Rational Function Spaces.- Appendix A1 Algorithms and Computational Concerns.- Appendix A2 Orthogonality and Irrationality.- Appendix A3 An Interpolation Theorem.- Appendix A5 Inequalities for Polynomials with Constraints.- Notation.