Interpolation Processes Basic Theory and Applications /

The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric a...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Mastroianni, Giuseppe (Autor), Milovanovic, Gradimir (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Springer Monographs in Mathematics,
Temas:
Integral equations.
Special functions.
Sequences (Mathematics).
Fourier analysis.
Integral Equations.
Special Functions.
Sequences, Series, Summability.
Fourier Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 1. Constructive Elements and Approaches in Approximation Theory
  • 1.1 Introduction to Approximation Theory
  • 1.2 Basic Facts on Trigonometric Approximation
  • 1.3 Chebyshev Systems and Interpolation
  • 1.4 Interpolation by Algebraic Polynomials
  • 2. Orthogonal Polynomials and Weighted Polynomial Approximation
  • 2.1 Orthogonal Systems and Polynomials
  • 2.2 Orthogonal Polynomials on the Real Line
  • 2.3 Classical Orthogonal Polynomials
  • 2.4 Nonclassical Orthogonal Polynomials
  • 2.5 Weighted Polynomial Approximation
  • 3. Trigonometric Approximation
  • 3.1 Approximating Properties of Operators
  • 3.2 Discrete Operators
  • 4. Algebraic Interpolation in Uniform Norm
  • 4.1 Introduction and Preliminaries
  • 4.2 Optimal Systems of Nodes
  • 4.3 Weighted Interpolation
  • 5. Applications
  • 5.1 Quadrature Formulae
  • 5.2 Integral Equations
  • 5.3 Moment-Preserving Approximation
  • 5.4 Summation of Slowly Convergent Series
  • References
  • Index.

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