Displaying similar documents to “On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms”

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Xuan Thao, Nguyen, Kim Tuan, Vu, Thanh Hong, Nguyen (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 44A05, 44A35 With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.

Solving singular convolution equations using the inverse fast Fourier transform

Eduard Krajník, Vincente Montesinos, Peter Zizler, Václav Zizler (2012)

Applications of Mathematics

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The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.

A note on the convolution theorem for the Fourier transform

Charles S. Kahane (2011)

Czechoslovak Mathematical Journal

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In this paper we characterize those bounded linear transformations T f carrying L 1 ( ℝ 1 ) into the space of bounded continuous functions on ℝ 1 , for which the convolution identity T ( f * g ) = T f · T g holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.