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Approximation Theory Using Positive Linear Operators
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Librairie Eyrolles - Paris 5e

Approximation Theory Using Positive Linear Operators

Approximation Theory Using Positive Linear Operators

Radu Paltanea

210 pages, parution le 31/10/2004


This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, particularly as it affects computer-aided geometric design. In this book, the crucial role of the second order moduli of continuity in the study of such operators is emphasized. New and efficient methods, applicable to general operators and to diverse concrete moduli, are presented. The advantages of these methods consist in obtaining improved and even optimal estimates, as well as in broadening the applicability of the results.

Additional Topics and Features:

  • Examination of the multivariate approximation case
  • Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators
  • Many general estimates, leaving room for future applications (e.g. the B-spline case)
  • Extensions to approximation operators acting on spaces of vector functions
  • Historical perspective in the form of previous significant results

This monograph will be of interest to those working in the field of approximation or functional analysis. Requiring only familiarity with the basics of approximation theory, the book may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject.

Written for:
Graduate students, postdocs and higher qualified scientists in mathematics and computer science interested in the fields of Geometric Modeling, Computer Aided Geometric Design, Image Processing, Real Analysis and Approximation Theory


  • Introduction
  • Estimates with second order moduli
  • Absolute optimal constants
  • Estimates for the Bernstein operators
  • Two classes of Bernstein type operators
  • Approximation operators for vector valued function
  • References
Voir tout

Caractéristiques techniques

Éditeur(s) Birkhäuser
Auteur(s) Radu Paltanea
Parution 31/10/2004
Nb. de pages 210
Format 15 x 23,5
Couverture Broché
Poids 370g
Intérieur Noir et Blanc
EAN13 9780817643508
ISBN13 978-0-8176-4350-8


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