Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Xuan Thao, Nguyen; Kim Tuan, Vu; Thanh Hong, Nguyen

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Displaying similar documents to “Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations”

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...

Integral transforms of Fourier cosine and sine generalized convolution type.

Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Thanh Hong (2007)

International Journal of Mathematics and Mathematical Sciences

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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.

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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New Ramanujan-type formulas and quasi-Fibonacci numbers of order 7.

Wituła, Roman, Słota, Damian (2007)

Journal of Integer Sequences [electronic only]

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On the solution of some non-local problems

F. Criado, Jr. Criado, F., N. Odishelidze (2004)

Czechoslovak Mathematical Journal

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This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution...