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Lp-general approximations by multivariate singular integral operators

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Języki publikacji
EN
Abstrakty
EN
In this article, we study the Lp, 1 ≤ p < ∞ approximation properties of general multivariate singular integral operators over RN, N ≥ 1. We establish their convergence to the unit operator with rates. 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 where this theory can be applied directly.
Wydawca
Rocznik
Strony
491--502
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
  • Department of Mathematical Sciences, University of Memphis, Memphis, Tn 38152, U.S.A.
Bibliografia
  • [1] G. Anastassiou, Lp convergence with rates of smooth Picard singular operators, Differential and difference equations and applications, Hindawi Publ. Corp., New York, (2006), 31–45.
  • [2] G. Anastassiou, General uniform approximation theory by multivariate singular integral operators, submitted, 2010.
  • [3] G. Anastassiou, O. Duman, Statistical Lp-approximation by double Gauss–Weierstrass singular integral operators, Comput. Math. Appl. 59 (2010), 1985–1999.
  • [4] G. Anastassiou, O. Duman, Statistical Lp-convergence of double smooth Picard singular integral operators, J. Comput. Anal. Appl., accepted for publication, 2010.
  • [5] G. Anastassiou, S. Gal, Approximation Theory, Birkhaüser, Boston, Basel, Berlin, 2000.
  • [6] G. Anastassiou, R. Mezei, Lp convergence with rates of smooth Gauss–Weierstrass singular operators, Nonlinear Studies, to appear 2010.
  • [7] G. Anastassiou. R. Mezei, Lp convergence with rates of smooth Poisson–Cauchy type singular operators, International Journal of Mathematical Sciences, accepted, 2010.
  • [8] G. Anastassiou, R. Mezei, Lp convergence with rates of general singular integral operators, submitted, 2010.
  • [9] J. Edwards, A Treatise on the Integral Calculus, Vol. II, Chelsea, New York, 1954.
  • [10] S. G. Gal, Remark on the degree of approximation of continuous functions by singular integrals, Math. Nachr. 164 (1993), 197–199.
  • [11] R. N. Mohapatra, R. S. Rodriguez, On the rate of convergence of singular integrals for Hölder continuous functions, Math. Nachr. 149 (1990), 117–124.
  • [12] D. Zwillinger, CRC Standard Mathematical Tables and Formulae, 30th edition, Chapman & Hall/CRC, Boca Raton, 1995.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e79f3c7e-72c6-4a1a-9a5e-d4772bc87dd1
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