Polynomials and polynomial inequalities
著者
書誌事項
Polynomials and polynomial inequalities
（Graduate texts in mathematics, 161）
Springer-Verlag, c1995
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注記
Includes bibliographical references (p. [448]-466) and index
内容説明・目次
内容説明
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 Muntz 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.
目次
Chaptern 1 Introduction and Basic Properties.- 2 Some Special Polynomials.- 3 Chebyshev and Descartes Systems.- 4 Denseness Questions.- 5 Basic Inequalities.- 6 Inequalities in Muntz 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.
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