# Approximation by Multivariate Singular Integrals

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

*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. This book is appropriate for researchers and selected seminars at the graduate level.

Gauss-Weierstrass Korovkin type approximation theorem Voronovskaya type multivariate singular integrals

- DOI https://doi.org/10.1007/978-1-4614-0589-4
- Copyright Information George A. Anastassiou 2011
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4614-0588-7
- Online ISBN 978-1-4614-0589-4
- Series Print ISSN 2191-8198
- Series Online ISSN 2191-8201
- Buy this book on publisher's site

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