Norm inequalities for new convolutions and their applications

Duc, Dinh Thanh; Nhan, Nguyen Du Vi

doi:10.2298/aadm150109001d

Cited by 12 publications

(2 citation statements)

References 7 publications

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“…Regarding the convolutions, in some other studies, there is the application of other methods with weighted Lebesgue spaces in which is possible to obtain norm inequalities among some L p -spaces. This is the case of the works [17,12,14], in which, at least in one of them, are also used methods of reproducing kernel Hilbert spaces. The present work proposes a different approach although containing some of the goals of those other works.…”

Section: Introductionmentioning

confidence: 99%

Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula

Castro

Guerra

Tuan

2019

Mathematica Slovaca

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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.

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Section: Introductionmentioning

confidence: 99%

Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula

Castro

Guerra

Tuan

2019

Mathematica Slovaca

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“…In some interesting cases of integral equations (25) and (26), relations between functions F and f can be obtained in other, more specific form. For example, consider the following generalization of Duc and Nhan [11,Example 4] integral equation…”

Section: Estimating Solutions Of Certain Types Of Integral Equationsmentioning

confidence: 99%

Archives of Control Sciences

Różański,

Sikora,

Smuda

et al. 2021

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The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel's integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel's integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel's integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel's formula in the theory of operator semigroups is given. Some applications of Duhamel's formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel's integral for differential equations with fractional order derivative.

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