We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series representations for the characteristic function and for the density of a free stable distribution. All of these formulas bear close resemblance to the corresponding expre...

The cone beam transform of a tensor field of order m in n >/= 2 dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of the n-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces for m = 0 and n = 3 to the well-known formula of Grangeat. In that sense, the paper contains a ge...

In this paper, we use Mellin transform to get the expression for the free boundary an price of an American finite-lived option, when the underlying is govern by the Levy process. We have also derived the free boundary and price of an American perpetual put as the limit of the preceded finite-lived option. We then show how to compute the price of an American option on a basket of stocks using Me...

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...

A paper currency recognition system has a wide range of applications such as self receiver machines for automated teller machines and automatic good-selling machines. In this paper a new paper currency recognition system based on Fourier-Mellin transform, Markovian characteristics and Support Vector Machine (SVM) is presented. In the first, a pre-processing algorithm by Fourier-Mellin transform...

In [14], P.Schapira obtained a formula for RS in the general situation. This formula gives an inversion formula for the Radon transform of constructible functions from a real projective space to its dual in the case when the whole dimension is odd. We can, that is, reconstruct a constructible function φ on the projective space from its Radon transform RS(φ). This topological meaning is that we ...

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on R. 2000 ...

We hear vowels pronounced by men and women as approximately the same although the length of the vocal tract varies considerably from group to group. At the same time, we can identify the speaker group. This suggests that the auditory system can extract and separate information about the size of the vocal-tract from information about its shape. The duration of the impulse response of the vocal t...

This paper investigates the American strangle option in a mean-reversion environment. When underlying asset follows mean-reverting lognormal process, an analytic pricing formula for is explicitly provided. To present formula, we consider partial differential equation (PDE) options with two optimal stopping boundaries and use Mellin transform techniques to derive integral representation arising ...