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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 3, Pages 153-158

On the convolution product of the distributional kernel Kα,β,γ,ν

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 18 June 2001; Revised 19 February 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a distributional kernel Kα,β,γ,ν which is related to the operator k iterated k times and defined by k=[(r=1p2/xr2)4(j=p+1p+q2/xj2)4]k, where p+q=n is the dimension of the space n of the n-dimensional Euclidean space, x=(x1,x2,,xn)n, k is a nonnegative integer, and α, β, γ, and ν are complex parameters. It is found that the existence of the convolution Kα,β,γ,νKα,β,γ,ν is depending on the conditions of p and q.