R. A. Lorentz, Ed.,George G. Lorentz: Mathematics from Leningrad to Austin
✍ Scribed by Vilmos Totik
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 87 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
are derived in terms of suitably defined K-functionals. Various expressions for these K-functionals are given in Chapter 5. Chapter 6, one of the central chapters, is devoted to the question where the supremum norm and the L p -norms of weighted polynomials wP, P # 6 n , live.
Chapter 7 deals with the problem of approximation of entire functions, while Chapter 8 contains further technical results regarding Freud polynomials. In Chapter 9, these results are applied to the study of orthogonal polynomial expansions, polynomials of Lagrange interpolation, and quadrature processes. The closure of certain weighted polynomials and the asymptotic behavior of the leading coefficients of the Freud polynomials are studied in Chapter 10. The last chapter, Chapter 11, contains the theory of weighted polynomials of the form w n P, P # 6 n , of the incomplete polynomials, and applications in the theory of neural networks and wavelets. The book concludes with a short appendix about theorems from functional analysis, potential theory, the theory of Fourier series, approximation theory and the Bernstein approximation problem on the real line.
No references are given in the main text, but the historical notes for each chapter and the credits are collected in the notes following the appendix.
I have enjoyed reading this monograph, and I recommend it for all students and scholars interested in analysis and approximation theory.