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Other titles in the Springerbriefs in Mathematics series:

Springerbriefs in Mathematics #3: Approximation by Multivariate Singular Integrals

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Springerbriefs in Mathematics #3: Approximation by Multivariate Singular Integrals Cover

 

Synopses & Reviews

Publisher Comments:

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations.

Table of Contents

-1. Uniform Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications, References). -2. Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications, References). -3. Global Smoothness Preservation and Simultaneous Approximation by Multivariate General Singular Integrals(Introduction, Main Results, Applications, References). -4. Multivariate Voronovskaya Asymptotic Expansions for General Singular Integrals (Introduction, Main Results, Applications, References).-5. Simultaneous Approximation by Multivariate Complex General Singular Integrals (Introduction, Main Results, Applications, References). -6. Approximation of Functions of Two Variables via Almost Convergence of Double Sequences (Introduction and Preliminaries, Korovkin type approximation theorem, Some consequences, References).

Product Details

ISBN:
9781461405887
Author:
Anastassiou, George A
Publisher:
Springer
Author:
Anastassiou, George A.
Subject:
Mathematics-Differential Equations
Subject:
Mathematical Analysis
Subject:
Gauss-Weierstrass
Subject:
Korovkin type approximation theorem
Subject:
Voronovskaya type
Subject:
multivariate singular integrals
Subject:
Integral Transforms, Operational Calculus
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Probability Theory and Stochastic Processes
Copyright:
Edition Description:
2011
Series:
SpringerBriefs in Mathematics
Publication Date:
20110831
Binding:
TRADE PAPER
Language:
English
Pages:
89
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Numeric Analysis
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Springerbriefs in Mathematics #3: Approximation by Multivariate Singular Integrals Used Trade Paper
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