Associated with a given suitable function, or a measure, on R, we introduce a correlation function so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation ...

Impulse response functions (IRFs) and frequency response functions (FRFs) are fundamental quantities that describe the dynamic behaviour of a linear vibrating system in the time and frequency domains respectively. The ...

We introduce an explicit representation of the double affine Hecke algebra (of type A(1)) at q = 1 that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra. (C) ...

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement ...

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz ...

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a ...

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a ...

In this paper, we will present a new and modi ed extended classical Gamma, Beta functions. Some properties basic are studied, such as the integral representations, functional relations and we will evaluate the action of ...