Polynomials and Polynomial Inequalities / Edition 1

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Overview

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 M√ľntz 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 round off the text. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.

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Editorial Reviews

From the Publisher
"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
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Product Details

  • ISBN-13: 9780387945095
  • Publisher: Springer New York
  • Publication date: 9/27/1995
  • Series: Graduate Texts in Mathematics Series , #161
  • Edition description: 1995
  • Edition number: 1
  • Pages: 480
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.13 (d)

Table of Contents

Preface
Ch. 1 Introduction and Basic Properties 1
Ch. 2 Some Special Polynomials 29
Ch. 3 Chebyshev and Descartes Systems 91
Ch. 4 Denseness Questions 154
Ch. 5 Basic Inequalities 227
Ch. 6 Inequalities in Muntz Spaces 275
Ch. 7 Inequalities for Rational Function Spaces 320
Appendix A1 Algorithms and Computational Concerns 356
Appendix A2 Orthogonality and Irrationality 372
Appendix A3 An Interpolation Theorem 382
Appendix A4 Inequalities for Generalized Polynomials in L[subscript p] 392
Appendix A5 Inequalities for Polynomials with Constraints 417
Bibliography 448
Notation 467
Index 473
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