Polynomials and Polynomial Inequalities

  • Peter Borwein
  • Tamás Erdélyi

Part of the Graduate Texts in Mathematics book series (GTM, volume 161)

Table of contents

  1. Front Matter
    Pages i-x
  2. Peter Borwein, Tamás Erdélyi
    Pages 1-28
  3. Peter Borwein, Tamás Erdélyi
    Pages 29-90
  4. Peter Borwein, Tamás Erdélyi
    Pages 91-153
  5. Peter Borwein, Tamás Erdélyi
    Pages 154-226
  6. Peter Borwein, Tamás Erdélyi
    Pages 227-274
  7. Peter Borwein, Tamás Erdélyi
    Pages 275-319
  8. Peter Borwein, Tamás Erdélyi
    Pages 320-355
  9. Back Matter
    Pages 356-482

About this book

Introduction

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.

Keywords

algebra algebraic geometry complex analysis interpolation number theory

Authors and affiliations

  • Peter Borwein
    • 1
  • Tamás Erdélyi
    • 2
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0793-1
  • Copyright Information Springer-Verlag New York, Inc. 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94509-5
  • Online ISBN 978-1-4612-0793-1
  • Series Print ISSN 0072-5285
  • About this book