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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 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 study the spectrum of the distributional kernel Kα,β(x), where α and β are complex numbers and x is a point in the space n of the n-dimensional Euclidean space. We found that for any nonzero point ξ that belongs to such a spectrum, there exists the residue of the Fourier transform (1)kK2k,2k(ξ)ˆ, where α=β=2k, k is a nonnegative integer and ξn.