A new approach to seismic migration formalizes the classical diffraction (or common-tangent) stack by relating it to linearized seismic inversion and the generalized Radon transform. This approach recasts migration as the problem of reconstructing the earth’s acoustic scattering potential from its integrals over isochron surfaces. The theory rests on a solution of the wave equation with the geo...

The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some n...

We give the inversion formula and Plancherel for hypergeometric Fourier transform associated with a root system of type $BC$, when multiplicity parameters are not necessarily non-negative.

For any α-stable Lévy process with jumps on both sides, where α ∈ (1, 2), we find the Mellin transform of the first hitting time of the origin and give an expression for its density. This complements existing work in the symmetric case and the spectrally one-sided case; cf. [38, 19] and [33, 36], respectively. We appeal to the Lamperti– Kiu representation of Chaumont et al. [16] for real-valued...

The steady-state waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steady-state waiting time in the GI/G/1 queue is characterized by Spitzer’s (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contour-integral expression for the Laplace transform of the GI/G/1 steady-state waiting...

A three parameter family of probability distributions is constructed such that its Mellin transform defined over the same domain as 2D GMC on Riemann sphere with insertion points $(\alpha_1,\alpha_2,\alpha_3)$ and satisfies DOZZ formula in sense Kupiainen (Ann. Math. 191 (2020) 81 -- 166). The are products independent Fyodorov-Bouchaud powers Barnes beta types $(2, 1)$ 2).$ In special case $\al...

It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further definition based on Mellin transform and it can be used when applied to radial functions. The main finding tested case space-fractional diffusion equation. one-dimensional also considered, such Riesz (namely symmetric Riesz–Feller) derivative established. This ...