Integral Transforms Related to a Generalized Convolution
Copyright policy )Integral Transforms Related to a Generalized Convolution
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.
- Kuwait University Kuwait
Convolution as an integral transform, convolution transform, Bessel function as kernel, Anger-Weber function as kernel, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Plancherel theorem, Watson theorem, Fourier cosine and sine transforms, Airy function as kernel
Convolution as an integral transform, convolution transform, Bessel function as kernel, Anger-Weber function as kernel, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Plancherel theorem, Watson theorem, Fourier cosine and sine transforms, Airy function as kernel
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).21 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!