Integral transforms of Fourier cosine and sine generalized convolution type.

Nguyen Xuan Thao; Vu Kim Tuan; Nguyen Thanh Hong

Displaying similar documents to “Integral transforms of Fourier cosine and sine generalized convolution type.”

On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.

Nguyen Xuan Thao (2010)

Mathematical Problems in Engineering

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On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms

Nguyen Thanh Hong, Trinh Tuan, Nguyen Xuan Thao (2013)

Applications of Mathematics

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We deal with several classes of integral transformations of the form $f (x) \to D \int_{ℝ_{+}^{2}} \frac{1}{u} (e^{- u cosh (x + v)} + e^{- u cosh (x - v)}) h (u) f (v) d u d v,$ where $D$ is an operator. In case $D$ is the identity operator, we obtain several operator properties on $L_{p} (ℝ_{+})$ with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on $L_{2} (ℝ_{+})$ and define the inversion formula. Further, for an other class of differential operators...

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.