An analytical inversion formula for the exponential Radon transform with an imaginary attenuation coefficient was developed in 2007 (2007 Inverse Problems 23 1963-71). The inversion formula in that paper suggested that it is possible to obtain an exact MRI (magnetic resonance imaging) image without acquiring low-frequency data. However, this un-measured low-frequency region (ULFR) in the k-spac...

We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: T ((an))n = 1/(a0 + · · ·+an). We determine the corresponding measure μ, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. The Mellin transform F of μ extends to a meromorphic function in the whole complex plane. It ca...

Let \begin{document}$ n\in \mathbb{N} $\end{document} and for every id="M2">\begin{document}$ w>0 let id="M3">\begin{document}$ K_{w}:\left( 0, \infty \right) ^{n}\rightarrow \mathbb{R} be Borel measurable kernels\begin{document}$ . Under suitable assumptions, the mult...

An attempt is made here to study the Mittag–Leffler function with two variables. Its various properties including integral and operational relationships other known functions of one variable, pure differential recurrence relations, Euler transform, Laplace Mellin Whittaker Mellin–Barnes representation, its relationship Wright hypergeometric are investigated established. Also, variables associat...

Space-variant optical processors are the subject of considerable research.1 One of the most promising methods by which such systems can be realized is the application of coordinate transformations to the input data.2' 3 The extension of this technique to produce optical Mellin transforms4 and distortion-invariant pattern-recognition systems has been reported over the past three years.k7 Of part...

With a change of variables the Abel transform gives the projection of a 2-D distribution with circular symmetry. Thus the Abel inversion formula allows one to determine the radial dependence of such a distribution from its projection. However, this inversion formula is very sensitive to noise in the projection data. When the projection data are derived from radiographic measurements, further di...

Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...

Fundamental solutions of space-time fractional diffusion equations can be interpret as probability density functions. This fact creates a strong link with stochastic processes. Recasting probability density functions in terms of subordination laws has emerged to be important to built up stochastic processes. In particular, for diffusion processes, subordination can be understood as a diffusive ...