Series in Approximations and Decompositions - Vol. 7
INTRODUCTION TO THE THEORY OF WEIGHTED POLYNOMIAL APPROXIMATION
by H N Mhaskar (California State University, Los Angeles)
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.
Contents:
- Orthogonal Polynomials
- Approximation on [–1,1]
- Freud
Polynomials
- Degree of Approximation
- The K-Functional
- Potential Theory
- Approximation of Entire Functions
- Freud Polynomials II
- Processes of Approximation
- A Density Theorem
- Applications
- Appendix
Readership: Mathematicians.
"Little preliminary knowledge is needed to understand the subject (mostly real and complex analysis), and the author provides all the information needed to make reading easier. The book is a good source of well-organized results all researchers in the field will benefit from."
| Mathematical Reviews, 1998 |
"I have enjoyed reading this monograph, and I recommend it for all students and scholars interested in analysis and approximation theory."
| Journal of Approximation Theory, 1998 |
| 396pp |
Pub. date: Jan 1997 |
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