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Al-Musallam, F.; Tuan, Vu Kim

Integral transforms related to a generalized convolution. (English) Zbl 0970.44004

Result. Math. 38, No. 3-4, 197-208 (2000).
A general convolution transform of the Fourier cosine-sine type is investigated. The authors find necessary and sufficient conditions on the kernel function, which makes the mentioned transform a unitary transform on \(L_2(\mathbb{R})\). A special class of the Fourier sine kernels is defined. Watson and Plancherel type theorems are proved. Interesting examples of convolutions, which are associated with the Airy, Anger-Weber and modified Bessel special functions as kernels are demonstrated.
Reviewer: Semyon Yakubovich (Porto)

Cited in 19 Documents

MSC:

44A35 Convolution as an integral transform
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords:

Fourier cosine and sine transforms; Plancherel theorem; Watson theorem; Airy function as kernel; Anger-Weber function as kernel; Bessel function as kernel; convolution transform
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References:

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