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On approximation properties of a family of linear operators at critical value of parameter
(Academic Press Inc Elsevier Science, 2006) Aliev, Ilham A.; Gadjiev, A. D.; Aral, Ali
We introduce the family of linear operators [GRAPHICS] associated to a certain "admissible bunch" of operators S-t, t > 0, acting on L-p (R-n, dm, and investigate the approximation properties of this family as alpha -> 0(+). We give some applications to the Riesz and the Bessel potentials generated by the ordinary (Euclidean) and generalized translations. (C) 2005 Elsevier Inc. All rights reserved.
On behaviour of the Riesz and generalized Riesz potentials as order tends to zero
(Element, 2007) Gadjiev, A. D.; Aral, A.; Aliev, Ilham A.
In this paper, we present the Riesz potentials I-alpha and the generalized Riesz potentials I-v(alpha) as the families of positive linear operators, depending on parameter alpha > 0. We investigate their pointwise convergence and convergence in the norm as alpha -> 0. We investigate also the order of approximation of these families and show in particular that the order of approximation at the Lipschitz points is independent from Lipschitz degree.