Author

# Nguyen Minh Tuan

Bio: Nguyen Minh Tuan is an academic researcher. The author has contributed to research in topics: Convolution & Fourier integral operator. The author has an hindex of 6, co-authored 12 publications receiving 97 citations.

##### Papers

More filters

••

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

••

TL;DR: In this article, a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra is given, and three convolutions are constructed for the Fourier transforms with geometric variables.

Abstract: This paper gives a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra, constructs three convolutions for the Fourier transforms with geometric variables and four generalized convolutions for the Fourier-cosine, Fourier-sine transforms. With respect to applications, by using the constructed convolutions normed rings on L1(Rn) are constructed, and explicit solutions of integral equations of convolution type are obtained (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

22 citations

••

Osaka University

^{1}TL;DR: In this paper, the explicit solutions of a class of singular integral equations with a linear-fractional Carleman shift and the degenerate kernel on the unit circle by means of the Riemann boundary value problem and a system of linear algebraic equations are considered.

Abstract: This article deals with the solvability, the explicit solutions of a class of singular integral equations with a linear-fractional Carleman shift and the degenerate kernel on the unit circle by means of the Riemann boundary value problem and of a system of linear algebraic equations. All cases about index of the coefficients in the equations are considered in detail.

19 citations

••

TL;DR: In this article, it was shown that any Hermite function or linear combination of those functions is a weight function of four explicit generalized convolutions for the Fourier cosine and sine transforms, and sufficient and necessary conditions for the solvability and explicit solutions of integral equations of convolution type are provided by using the constructed convolutions.

Abstract: In this paper, we show that arbitrary Hermite function or appropriate linear combination of those functions is a weight-function of four explicit generalized convolutions for the Fourier cosine and sine transforms. With respect to applications, normed rings on \({L^1(\mathbb{R}^d)}\) are constructed, and sufficient and necessary conditions for the solvability and explicit solutions in \({L^1(\mathbb{R}^d)}\) of the integral equations of convolution type are provided by using the constructed convolutions.

15 citations

••

TL;DR: In this article, six new generalized convolutions of the integral transforms of Fourier type were given, and a class of integral equations of convolution type by using the constructed convolutions was investigated.

Abstract: This article gives six new generalized convolutions of the integral transforms of Fourier type, and investigates a class of integral equations of convolution type by using the constructed convolutions Namely, the explicit solutions in L 1(ℝ d ) of a class of integral equations of convolution type are obtained

8 citations

##### Cited by

More filters

•

01 Jan 1966

TL;DR: Boundary value problems in physics and engineering were studied in this article, where Chorlton et al. considered boundary value problems with respect to physics, engineering, and computer vision.

Abstract: Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

733 citations

••

TL;DR: In this article, the authors obtained new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform).

Abstract: We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.

50 citations

••

TL;DR: In this article, the quadratic Fourier transform was examined by analyzing corresponding six subcases of the transform within a reproducing kernel Hilbert spaces framework, and the results showed that the transform can be expressed as a generalized quadrastic function for one order parameter in the ordinary Fourier transformation.

Abstract: In this paper we shall examine the quadratic Fourier transform which is introduced by the generalized quadratic function for one order parameter in the ordinary Fourier transform. This will be done by analyzing corresponding six subcases of the quadratic Fourier transform within a reproducing kernel Hilbert spaces framework.

33 citations

••

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

••

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