00000cmm a22000004i 4500 UP-99796217611212130 Buklod 20250130101000.0 m go j cr |nu|||auu|a 250130s2011 nyu do j eng 9781461405894 (eBook) 1461405890 (eBook) (iLib)UPD-00214608300 DMLR rda eng DMLUC QA 403.5 A53 2011eb Anastassiou, George A. 1952- editor. Approximation by multivariate singular integrals [electronic resource] by George A. Anastassiou. New York, New York Springer New York 2011. 1 online resource (x, 79 pages) text rdacontent computer rdamedia online resource rdacarrier SpringerBriefs in Mathematics Includes bibliographical references. Uniform Approximation by General Multivariate Singular Integral Operators -- L p -Approximation by General Multivariate Singular Integral Operators -- Global Smoothness Preservation and Simultaneous Approximation by Multivariate General Singular Integrals -- Multivariate Voronovskaya Asymptotic Expansions for General Singular Integrals -- Simultaneous Approximation by Multivariate Complex General Singular Integrals -- Approximation of Functions of Two Variables via Almost Convergence of Double Sequences IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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 Singular integrals. Mathematics. SpringerLink (Online service). Electronic Resource Available for UP System via Springer Link. https://doi.org/10.1007/978-1-4614-0589-4 FO UPD DMLR QA 403.5 A53 2011eb Electronic Resource