Book contents
- Frontmatter
- Contents
- Preface
- List of notation
- 1 Best approximation and duality in extremal problems
- 2 Polynomials and spline functions as approximating tools
- 3 Comparison theorems and inequalities for the norms of functions and their derivatives
- 4 Polynomial approximation of classes of functions with bounded rth derivative in Lp
- 5 Spline approximation of classes of functions with a bounded rth derivative
- 6 Exact constants in Jackson inequalities
- 7 Approximation of classes of functions determined by modulus of continuity
- 8 N-widths of functional classes and closely related extremal problems
- Appendix
- References
- Index of notation
- Index
Preface
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Contents
- Preface
- List of notation
- 1 Best approximation and duality in extremal problems
- 2 Polynomials and spline functions as approximating tools
- 3 Comparison theorems and inequalities for the norms of functions and their derivatives
- 4 Polynomial approximation of classes of functions with bounded rth derivative in Lp
- 5 Spline approximation of classes of functions with a bounded rth derivative
- 6 Exact constants in Jackson inequalities
- 7 Approximation of classes of functions determined by modulus of continuity
- 8 N-widths of functional classes and closely related extremal problems
- Appendix
- References
- Index of notation
- Index
Summary
This book was written for the series Encyclopedia of Mathematics and Its Applications published in the USA and United Kingdom since 1974. A few years ago I was asked to write a monograph Exact Constants in Approximation Theory by the editor of the series Professor G.-C. Rota.
The purpose and objectives of the series were presented by the editorial board as their credo in the following statement:
It was not too long ago that the view that in present-day mathematics one can find the basic concepts of tomorrow's science was widely spread. Nowadays, however, mathematical results, proudly secured behind the barrier of complicated terminology with uncompromising strictness, are very often far removed from their potential users … The ample results along with sophisticated modern mathematical presentation have resulted in the mathematician's reluctance to view his achievements from aside, with the eyes of an interested applied scientist. This fact and our conviction that every science should sooner or later test itself by becoming mathematical are the motivating force of the Encyclopedia.
In their letter to authors the editorial board gives them a free choice of material and style of presentation imposing only two requirements that the monograph should meet, namely: (1) the content should not be of transient significance; and (2) the form of presentation should make the subject matter comprehensible for a wide circle of reades, including non-specialists who may be dealing with other branches of mathematics.
- Type
- Chapter
- Information
- Exact Constants in Approximation Theory , pp. ix - xiPublisher: Cambridge University PressPrint publication year: 1991