Polynomials And Polynomial Inequalities
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Author | : Peter Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 491 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461207932 |
Download Polynomials and Polynomial Inequalities Book in PDF, Epub and Kindle
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.
Author | : G. V. Milovanovi? |
Publisher | : World Scientific |
Total Pages | : 842 |
Release | : 1994 |
Genre | : Science |
ISBN | : 9789810204990 |
Download Topics in Polynomials Book in PDF, Epub and Kindle
The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
Author | : Robert B. Gardner |
Publisher | : Academic Press |
Total Pages | : 444 |
Release | : 2022-02-10 |
Genre | : Mathematics |
ISBN | : 012812007X |
Download Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials Book in PDF, Epub and Kindle
Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Markov-Bernstein-type inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions, and entire functions of exponential type Contains exhaustive references with more than five hundred citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research
Author | : Murray Marshall |
Publisher | : American Mathematical Soc. |
Total Pages | : 201 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844024 |
Download Positive Polynomials and Sums of Squares Book in PDF, Epub and Kindle
The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in $n$ variables with real coefficients, and many examples are included. Proofs are presented as clearly and as simply as possible. Various new, simpler proofs appear in the book for the first time. Abstraction is employed only when it serves a useful purpose, but, at the same time, enough abstraction is included to allow the reader easy access to the literature. The book should be essential reading for any beginning student in the area.
Author | : Lynn Marecek |
Publisher | : |
Total Pages | : |
Release | : 2020-05-06 |
Genre | : |
ISBN | : 9781951693848 |
Download Intermediate Algebra 2e Book in PDF, Epub and Kindle
Author | : Alexander Prestel |
Publisher | : Springer Science & Business Media |
Total Pages | : 269 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662046482 |
Download Positive Polynomials Book in PDF, Epub and Kindle
Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
Author | : James Fraser McKee |
Publisher | : Cambridge University Press |
Total Pages | : 350 |
Release | : 2008-05-08 |
Genre | : Mathematics |
ISBN | : 0521714672 |
Download Number Theory and Polynomials Book in PDF, Epub and Kindle
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Author | : Gradimir V. Milovanovic |
Publisher | : |
Total Pages | : 821 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download Topics in Polynomials Book in PDF, Epub and Kindle
Author | : Nikolaĭ Pavlovich Korneĭchuk |
Publisher | : Nova Publishers |
Total Pages | : 444 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9781560723615 |
Download Extremal Properties of Polynomials and Splines Book in PDF, Epub and Kindle
Extremal Properties of Polynomials & Splines
Author | : Herbert Stahl |
Publisher | : Cambridge University Press |
Total Pages | : 272 |
Release | : 1992-04-24 |
Genre | : Mathematics |
ISBN | : 9780521415347 |
Download General Orthogonal Polynomials Book in PDF, Epub and Kindle
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.