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Mirumbe, Ismail; Mango, John

On the convolution of some analytic functionals via the Fourier transform. (English) Zbl 1468.42004

Int. J. Adv. Appl. Math. Mech. 6, No. 3, 42-50 (2019).
Summary: In this paper, we use the Fourier transform, inverse Fourier transform and the distribution \(\xi^s\) in the \(\xi\)-line with support \(\{\xi \geq 0\}\) for \(s\) a complex number together with its meromorphic extension to prove the existence of the convolution of the distributions \(x^\lambda_+\) and \(x^\mu_-\) denoted by \(x^\lambda_+ \ast x^\mu_-\) where \(\mu\) and \(\lambda\) are complex parameters.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A85 Convolution, factorization for one variable harmonic analysis
46F10 Operations with distributions and generalized functions

Keywords:

Fourier transform; convolution; tempered distribution; boundary value distribution
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References:

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