Calderon reproducing formula associated with the Gegenbauer operator on the half-line

[摘要] In this paper, we introduce the generalized shift operator generated by the Gegenbauer differential operator D-lambda=(x(2) - 1)(1/2-lambda)d/dx(x(2)-1)(lambda+1/2) d/dx, and define a generalized convolution circle times on the half-line corresponding to the Gegenbauer differential operator. We investigate the Calderon reproducing formula associated with the convolution circle times involving finite Borel measures, leading to results on the L-p-norm and pointwise approximation for functions on the half-line. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] Gegenbauer differential operator;generalized shift operator;generalized convolution;Calderon reproducing formula