International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 12, Pages 715-723
On the spectrum of the distributional kernel related to the residue
Department of Mathematics, Chiangmai University, Chiangmai 50200, Thailand
Received 22 June 2000; Revised 26 February 2001
Copyright © 2001 Amnuay Kananthai. 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 study the spectrum of the distributional kernel , where and are complex numbers and is a point in the space of the -dimensional Euclidean space. We found that for any nonzero point that belongs to such a spectrum, there exists the residue of the Fourier transform , where , is a nonnegative integer and .