Simultaneous Approximation by Multivariate Complex General Singular Integrals
Chapter
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Abstract
Here, we present complex multivariate simultaneous approximation for general smooth singular integral operators converging with rates to the unit operator. The associated and presented inequalities are in ⋅ p , 1 ≤ p ≤ ∞ norm and they involve multivariate related moduli of smoothness. At the end, we list as this theory’s applicators the special cases of multivariate complex Picard, Gauss–Weierstrass, Poisson–Cauchy and Trigonometric singular integral operators. This chapter relies on [2].
References
- 1.G. Anastassiou, Global smoothness preservation and simultaneous approximation for multivariate general singular integral operators, Applied Math. Letters, 24(2011), 1009-1016.MATHCrossRefMathSciNetGoogle Scholar
- 2.G. Anastassiou, Multivariate Complex General Singular Integral Operators Simultaneous Approximation, Journal of Concrete and Applicable Mathematics, accepted, 2010.Google Scholar
- 3.G. Anastassiou, General uniform Approximation theory by multivariate singular integral operators, submitted, 2011.Google Scholar
- 4.G. Anastassiou, L p -general approximations by multivariate singular integral operators, submitted, 2011.Google Scholar
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© George A. Anastassiou 2011