Tuan Minh - Academia.edu (original) (raw)
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Papers by Tuan Minh
Opuscula Mathematica, 2012
This paper introduces a general concept of convolutions by means of the theory of reproducing ker... more This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
AIP Conference Proceedings, 2017
This paper presents new convolutions for the fractional Fourier transform which are somehow assoc... more This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.
Mathematica Slovaca
This paper considers two finite integral transforms of Fourier-type, in view to propose a set of ... more This paper considers two finite integral transforms of Fourier-type, in view to propose a set of eight new convolutions, and to analyze the solvability of a class of the integral equations of Wiener-Hopf plus Hankel type, defined on finite intervals, which is involved in engineering problems. The solvability and solution of the considered equations are investigated by means of Fourier-type series, and a Shannon-type sampling formula is obtained. Some concluding remarks with respect to theoretical issues and engineering applications are emphasized in the last section, along with the analysis of some illustrative cases, which exemplify that the present method solves cases which are not under the conditions of previously known techniques.
Scientiae Mathematicae Japonicae, Jul 1, 2009
World Bank, PREM Note, Public Sector Governance, …, 2007
Abstract. This article studies the existence of solutions to systems of nonlinear integro-differe... more Abstract. This article studies the existence of solutions to systems of nonlinear integro-differential self-referred and heredity equations. We show the existence of a global solution and the uniqueness of a local solution to a system of integro-differential equations with given initial conditions.
Opuscula Mathematica, 2012
This paper introduces a general concept of convolutions by means of the theory of reproducing ker... more This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
AIP Conference Proceedings, 2017
This paper presents new convolutions for the fractional Fourier transform which are somehow assoc... more This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.
Mathematica Slovaca
This paper considers two finite integral transforms of Fourier-type, in view to propose a set of ... more This paper considers two finite integral transforms of Fourier-type, in view to propose a set of eight new convolutions, and to analyze the solvability of a class of the integral equations of Wiener-Hopf plus Hankel type, defined on finite intervals, which is involved in engineering problems. The solvability and solution of the considered equations are investigated by means of Fourier-type series, and a Shannon-type sampling formula is obtained. Some concluding remarks with respect to theoretical issues and engineering applications are emphasized in the last section, along with the analysis of some illustrative cases, which exemplify that the present method solves cases which are not under the conditions of previously known techniques.
Scientiae Mathematicae Japonicae, Jul 1, 2009
World Bank, PREM Note, Public Sector Governance, …, 2007
Abstract. This article studies the existence of solutions to systems of nonlinear integro-differe... more Abstract. This article studies the existence of solutions to systems of nonlinear integro-differential self-referred and heredity equations. We show the existence of a global solution and the uniqueness of a local solution to a system of integro-differential equations with given initial conditions.