Parseval's formula and inversion formula for the S-transform are given. A relation between the S-transform and pseudodifferential operators is obtained. The S-transform is studied on the spaces S(ℝn) and S'(ℝn).

An inversion formula was developed by Bukhgeim and Kazantsev for attenuated fan-beam projections [Russian Academy of Science Siberian Branch: The Sobolev Institute of Mathematics (2002)]. The inversion formula was obtained by relating the attenuated fan-beam projections to unattenuated fan-beam projections and by trickily processing the unattenuated fan-beam projections. We show in this paper t...

The asymptotic distribution of the diameter of the digraph of a uniformly distributed random mapping of an n-element set to itself is represented as the distribution of a functional of a re ecting Brownian bridge. This yields a formula for the Mellin transform of the asymptotic distribution, generalizing the evaluation of its mean by Flajolet and Odlyzko (1990). Titre: La loi limite du diam etr...

In this paper, we consider the conical Radon transform on all one-sided circular cones in $$\mathbf{R}^3$$ with horizontal central axis whose vertices are a vertical line. We derive an explicit inversion formula for such transform. The makes use of slice sphere and V-line plane.

My assignment is going to introduce the Mellin transform and its application on harmonic sums [1]. Hjalmar Mellin(1854-1933, [2] for a summary of his works) gave his name to the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete prob...