Author

# Nguyen Xuan Thao

Other affiliations: Hanoi University, Water Resources University

Bio: Nguyen Xuan Thao is an academic researcher from Hanoi University of Science and Technology. The author has contributed to research in topics: Sine and cosine transforms & Convolution. The author has an hindex of 7, co-authored 22 publications receiving 141 citations. Previous affiliations of Nguyen Xuan Thao include Hanoi University & Water Resources University.

##### Papers

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01 Jan 1998

TL;DR: A generalized convolution for the Fourier cosine and sine transforms is introduced in this paper, and its properties and applications to integral equations are considered in this paper. But it is not shown how to apply it to the sine transform problem.

Abstract: A generalized convolution for the Fourier cosine and sine transforms is introduced its properties and applications to integral equations are considered

38 citations

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TL;DR: In this paper, a generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced, and its properties and applications to solving a system of integral equations are considered.

Abstract: A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

22 citations

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TL;DR: The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced in this paper, and its properties and applications to solving system of integral equations are considered.

Abstract: The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced. Its properties and applications to solving system of integral equations are considered.

21 citations

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TL;DR: In this paper, a generalized convolution was used to solve a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations.

Abstract: from Lp(R+) to Lq(R+), (1 6 p 6 2, p−1 + q−1 = 1) 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. Mathematics Subject Classification: 44A05, 44A35

11 citations

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TL;DR: Watson's and Plancherel's theorems are obtained on integral transforms of the form f ( x) ↦ g ( x ) = ( 1 − d 2 / d x 2) .

Abstract: Integral transforms of the form
f ( x ) ↦ g ( x ) = ( 1 − d 2 / d x 2 ) { ∫ 0 ∞ k 1 ( y ) [ f ( | x + y − 1 | ) + f ( | x − y + 1 | ) − f ( x + y + 1 ) − f ( | x − y − 1 | ) ] d y + ∫ 0 ∞ k 2 ( y ) [ f ( x + y ) + f ( | x − y | ) ] d y } from L p ( ℝ + ) to L q ( ℝ + ) , ( 1 ≤ p ≤ 2 , p − 1 + q − 1 = 1 ) are studied. Watson's and Plancherel's
theorems are obtained.

10 citations

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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 paper, the operational properties of two integral transforms of Fourier type were presented, and the formulation of convolutions for those transforms were derived and applied to linear partial differential equations and an integral equation with mixed Toeplitz-Hankel kernel.

Abstract: In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on \(L_{1}({\mathbb{R}})\), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.

27 citations

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TL;DR: In this article, the necessary and sufficient conditions for the solvability of two integral equations of convolution type were presented, the first equation generalizes from integral equations with the Gaussian kernel, and the second one contains the Toeplitz plus Hankel kernels.

26 citations

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TL;DR: In this article, the Fourier convolution type g(x) = ∫ ∞ 0 (k(x + y) + k(|x − y|))f(y)dy, x ∈ R +, is considered.

25 citations