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- catalog abstract "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.".
- catalog contributor b8518140.
- catalog contributor b8518141.
- catalog created "1995.".
- catalog date "1995".
- catalog date "1995.".
- catalog dateCopyrighted "1995.".
- catalog description "Ch. 1. Introduction and Basic Properties -- Ch. 2. Some Special Polynomials -- Ch. 3. Chebyshev and Descartes Systems -- Ch. 4. Denseness Questions -- Ch. 5. Basic Inequalities -- Ch. 6. Inequalities in Muntz Spaces -- Ch. 7. Inequalities for Rational Function Spaces -- Appendix A1 Algorithms and Computational Concerns -- Appendix A2 Orthogonality and Irrationality -- Appendix A3 An Interpolation Theorem -- Appendix A4 Inequalities for Generalized Polynomials in L[subscript p] -- Appendix A5 Inequalities for Polynomials with Constraints.".
- catalog description "Includes bibliographical references (p. [448]-466) and index.".
- catalog description "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.".
- catalog extent "x, 480 p. ;".
- catalog identifier "0387945091 (alk. paper)".
- catalog isPartOf "Graduate texts in mathematics ; 161".
- catalog issued "1995".
- catalog issued "1995.".
- catalog language "eng".
- catalog publisher "New York : Springer Verlag,".
- catalog subject "515/.252 20".
- catalog subject "Algebra.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Inequalities (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "Polynomials.".
- catalog subject "QA241 .B775 1995".
- catalog tableOfContents "Ch. 1. Introduction and Basic Properties -- Ch. 2. Some Special Polynomials -- Ch. 3. Chebyshev and Descartes Systems -- Ch. 4. Denseness Questions -- Ch. 5. Basic Inequalities -- Ch. 6. Inequalities in Muntz Spaces -- Ch. 7. Inequalities for Rational Function Spaces -- Appendix A1 Algorithms and Computational Concerns -- Appendix A2 Orthogonality and Irrationality -- Appendix A3 An Interpolation Theorem -- Appendix A4 Inequalities for Generalized Polynomials in L[subscript p] -- Appendix A5 Inequalities for Polynomials with Constraints.".
- catalog title "Polynomials and polynomial inequalities / Peter Borwein, Tamas Erdēlyi.".
- catalog type "text".