## OP-SF WEB

### Extract from OP-SF NET

Polynomials and Polynomial Inequalities
By P. Borwein and T. Erd\'elyi
Graduate Texts in Mathematics 161, Springer, Berlin, 1995, 480 pp.,
hardcover DM 98, ISBN 0-387-94509-1
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, focusing 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 M\"untz 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.
Contents:
Introduction and Basic Properties
Some Special Polynomials
Chebyshev and Descartes Systems
Denseness Questions
Basic Inequalities
Inequalities in M\"untz Spaces
Inequalities in Rational Function Spaces
Appendices:
Algorithms and Computational Concerns
Orthogonality and Irrationality
An Interpolation Theorem
Inequalities for Generalized Polynomials
Inequalities for Polynomials with Constraints.
Wolfram Koepf

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