Author

# Nguyen Thanh Hong

Other affiliations: University of Education, Winneba

Bio: Nguyen Thanh Hong is an academic researcher from Hanoi National University of Education. The author has contributed to research in topics: Convolution & Sine and cosine transforms. The author has an hindex of 5, co-authored 16 publications receiving 71 citations. Previous affiliations of Nguyen Thanh Hong include University of Education, Winneba.

##### Papers

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TL;DR: In this article, an interpolation formula for functions in the Hardy space on the right-half plane was proposed and proved to converge in norm and pointwise under a general condition.

Abstract: We introduce an interpolation formula for functions in the Hardy space on the right-half plane and prove its convergence in norm and pointwise under very general condition. We also obtain an inverse formula for the Laplace transform from data on a finite interval.

14 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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TL;DR: In this article, an integral transform related to a Fourier sine-Fourier - Fourier cosine generalized convolution was introduced, and a Watson type theorem for the transform was proved.

Abstract: We introduce an integral transform related to a Fourier sine-Fourier - Fourier cosine generalized convolution and prove a Watson type theorem for the transform. As applications we obtain solutions of some integral equations in closed form.

9 citations

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TL;DR: In this paper, the Toeplitz plus Hankel integral equation is solved in closed form with generalized convolutions. But the generalized convolution is not suitable for the case of generalized generalized generalized convexity.

Abstract: In this paper, we obtain solutions in closed form for some special cases of the Toeplitz plus Hankel integral equation with the help of generalized convolutions.

8 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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306 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