Author

# Le Xuan Huy

Bio: Le Xuan Huy is an academic researcher. The author has contributed to research in topics: Sine and cosine transforms & Two-sided Laplace transform. The author has an hindex of 2, co-authored 4 publications receiving 8 citations.

##### Papers

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TL;DR: In this article, generalized convolutions for the Fourier cosine, Fourier sine and Laplace integral transforms were introduced for solving integral equations and systems of integral equations are considered.

Abstract: In this paper we introduce two generalized convolutions for the Fourier cosine, Fourier sine and Laplace integral transforms. Convolution properties and their applications to solving integral equations and systems of integral equations are considered.

5 citations

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TL;DR: In this article, two classes of integral transforms related to two generalized convolutions for the Fourier cosine, Fourier sine and Laplace transforms are introduced and the Watson type theorem for these transforms is also obtained.

Abstract: In this paper, we introduce two classes of integral transforms related to two generalized convolutions for the Fourier cosine, Fourier sine and Laplace transforms. The Watson type theorem for these transforms is also obtained. As applications we apply these convolutions to solve some classes of integral and integro-differential equations.

5 citations

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TL;DR: In this paper, the authors introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms for solving a class of integral equations.

Abstract: In this paper, we introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms. Convolution properties and their applications for solving a class of integral equations and systems of integral equations are presented.

2 citations

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TL;DR: In this paper, several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms are considered.

Abstract: We introduce several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms. Some applications of these inequalities to estimate the solutions of some partial differential equations are considered. We also obtained solutions of a class of the Toeplitz plus Hankel integro-differential equations in closed form. Mathematics subject classification (2010): 33C10, 44A35, 45E10, 45J05, 47A30, 47B15.

2 citations

##### Cited by

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01 Mar 2009

TL;DR: In this paper, the relationship between these transforms and their properties was discussed and some important applications in physics and engineering were given, as well as their properties and applications in various domains.

Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

383 citations

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TL;DR: In this article, the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms are solved in closed form for a class of Fredholm integral equations with non-degenerate kernels.

Abstract: In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms.

3 citations

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3 citations

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TL;DR: In this paper, several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms are considered.

Abstract: We introduce several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms. Some applications of these inequalities to estimate the solutions of some partial differential equations are considered. We also obtained solutions of a class of the Toeplitz plus Hankel integro-differential equations in closed form. Mathematics subject classification (2010): 33C10, 44A35, 45E10, 45J05, 47A30, 47B15.

2 citations

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TL;DR: In this paper , two types of fractional Fourier-Laplace convolutions are defined, and corresponding fractional-fourier-laplace convolution theorems associated with the fractional cosine transform, fractional sine transform and Laplace transform are investigated in detail.

Abstract: In this paper, two types of fractional Fourier–Laplace convolutions are defined, and the corresponding fractional Fourier–Laplace convolution theorems associated with the fractional cosine transform (FRCT), fractional sine transform (FRST) and Laplace transform (LP) are investigated in detail. The relationship between the fractional Fourier–Laplace convolutions and the existing convolutions is given, and Young's type theorem as well as the weighted convolution inequality are also obtained. As an application for fractional Fourier–Laplace convolution, the filter design and the system of convolution-type integral equations are also considered, the computational complexity for the multiplicative filter is analysed, and explicit solutions for these equations are obtained.

1 citations