Polynomials and polynomial inequalities
By: Peter Borwein, Tamās Erdēlyi.
Contributors: Erdēlyi, Tāmas.
Series: Graduate texts in mathematics ;; 161
Publisher: Springer
Published: 1995
Place of publication: New York
Language: eng
Number of pages: 480
Subjects: Polynomials; Inequalities (Mathematics)
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.
Notes: Includes bibliographical references (p. [448]-466) and index.