On the spectrum of the distributional kernel related to the residue

Amnuay Kananthai

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-9

Abstract:

We study the spectrum of the distributional kernel K α , β ( x ) , where α and β are complex numbers and x is a point in the space ℝ 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 ) k K 2 k , 2 k ( ξ ) ˆ , where α = β = 2 k , k is a nonnegative integer and ξ ∈ ℝ n .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:597818

DOI: 10.1155/S0161171201011097

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