General uniform approximation theory by multivariate singular integral operators

• Autorzy: George A. Anastassiou
• Języki publikacji: EN

Abstrakty

EN

We study the uniform approximation properties of general multivariate singular integral operators on $ℝ^{N}$, N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 41A36: Approximation by positive operators
• 41A35: Approximation by operators (in particular, by integral operators)
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 1
• Strony: 15-25

Daty

wydano

2012

Twórcy

autor

George A. Anastassiou

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

Identyfikatory

DOI

10.4064/ap103-1-2