The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-co...The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.展开更多
In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Me...According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Mellin transform is also explored.The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain.It suits for the wideband underwater acoustic signal processing.展开更多
This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made ...The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients ?from the Taylor series are not changed to f(n)(0)?but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.展开更多
文摘The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
基金Sponsored by National Nature Science Foundation of China(10474079)
文摘According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Mellin transform is also explored.The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain.It suits for the wideband underwater acoustic signal processing.
文摘This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
文摘The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients ?from the Taylor series are not changed to f(n)(0)?but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.
