Introduction To The Theory Of Weighted Polynomial Approximation

H N Mhaskar

• Publisher: World Scientific
• Year: 1997
• Print ISBN: 9789810213121, 9789810213121
• eBook ISBN: 9789812832139
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Table of contents

• Contents
• Approximations and Decompositions
• Preface
• 1 Orthogonal Polynomials
• 2 Approximation on [-1,1]
• 3 Freud Polynomials
• 4 Degree of Approximation
• 5 The K-functional
• 6 Potential Theory
• 7 Approximation of Entire Functions
• 8 Freud Polynomials II
• 9 Processes of Approximation
• 10 A Density Theorem
• 11 Applications
• Appendix
• Notes
• References
• Subject Index
• Bibliography