02261nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002700139245010400166250001700270260004800287300002900335653003700364653003600401653004800437653002400485653003500509653004600544710003400590041001900624989003600643490003400679856007200713082001100785520115100796EB000363672EBX0100000000000000021672400000000000000.0cr|||||||||||||||||||||130626 ||| eng a97814614058941 aAnastassiou, George A.00aApproximation by Multivariate Singular IntegralshElektronische Ressourcecby George A. Anastassiou a1st ed. 2011 aNew York, NYbSpringer New Yorkc2011, 2011 aX, 79 pbonline resource aDistribution (Probability theory aDifferential equations, partial aProbability Theory and Stochastic Processes aIntegral Transforms aPartial Differential Equations aIntegral Transforms, Operational Calculus2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aSpringerBriefs in Mathematics uhttps://doi.org/10.1007/978-1-4614-0589-4?nosfx=yxVerlag3Volltext0 a515.72 aApproximation 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