Borwein P.B., Erdélyi T. Polynomials and Polynomial Inequalities

Springer, 1995. — 506 p. — (Graduate Texts in Mathematics) — ISBN 978-1-4612-0793-1.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.Some Special Polynomials
Chebyshev and Descartes Systems
Denseness Questions
Basic Inequalities
Inequalities in Müntz Spaces
Inequalities for Rational Function Spaces