Polynomials and Polynomial Inequalities / Edition 1

Polynomials and Polynomial Inequalities / Edition 1

by Peter Borwein, Tamas Erdelyi
     
 

ISBN-10: 0387945091

ISBN-13: 9780387945095

Pub. Date: 09/27/1995

Publisher: Springer New York

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

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

Product Details

ISBN-13:
9780387945095
Publisher:
Springer New York
Publication date:
09/27/1995
Series:
Graduate Texts in Mathematics Series, #161
Edition description:
1995
Pages:
480
Product dimensions:
9.21(w) x 6.14(h) x 1.13(d)

Table of Contents

Preface
Ch. 1Introduction and Basic Properties1
Ch. 2Some Special Polynomials29
Ch. 3Chebyshev and Descartes Systems91
Ch. 4Denseness Questions154
Ch. 5Basic Inequalities227
Ch. 6Inequalities in Muntz Spaces275
Ch. 7Inequalities for Rational Function Spaces320
Appendix A1 Algorithms and Computational Concerns356
Appendix A2 Orthogonality and Irrationality372
Appendix A3 An Interpolation Theorem382
Appendix A4 Inequalities for Generalized Polynomials in L[subscript p]392
Appendix A5 Inequalities for Polynomials with Constraints417
Bibliography448
Notation467
Index473

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