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Polynomials and Polynomial Inequalities

  • Textbook
  • © 1995

Overview

Authors:
  1. Peter Borwein

    1. Department of Mathematics and Statistics, Simon Fraser University, Burnaby, Canada

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  2. Tamás Erdélyi

    1. Department of Mathematics, Texas A&M University, College Station, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction and Basic Properties

    • Peter Borwein, Tamás Erdélyi
    Pages 1-28

  3. Some Special Polynomials

    • Peter Borwein, Tamás Erdélyi
    Pages 29-90

  4. Chebyshev and Descartes Systems

    • Peter Borwein, Tamás Erdélyi
    Pages 91-153

  5. Denseness Questions

    • Peter Borwein, Tamás Erdélyi
    Pages 154-226

  6. Basic Inequalities

    • Peter Borwein, Tamás Erdélyi
    Pages 227-274

  7. Inequalities in Müntz Spaces

    • Peter Borwein, Tamás Erdélyi
    Pages 275-319

  8. Inequalities for Rational Function Spaces

    • Peter Borwein, Tamás Erdélyi
    Pages 320-355

  9. Back Matter

    Pages 356-482
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Keywords

About this book

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.

Reviews

"This is a wonderful book which is strongly recommended for use in a class with students who are willing to work on the proofs, rather than to digest fully prepared and worked out proofs and examples." Jnl of Approximation Theory

Authors and Affiliations

  • Department of Mathematics and Statistics, Simon Fraser University, Burnaby, Canada

    Peter Borwein

  • Department of Mathematics, Texas A&M University, College Station, USA

    Tamás Erdélyi

Bibliographic Information

  • Book Title: Polynomials and Polynomial Inequalities

  • Authors: Peter Borwein, Tamás Erdélyi

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0793-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1995

  • Hardcover ISBN: 978-0-387-94509-5Published: 27 September 1995

  • Softcover ISBN: 978-1-4612-6902-1Published: 28 September 2012

  • eBook ISBN: 978-1-4612-0793-1Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 480

  • Topics: Analysis, Algebra

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