Related papers: The ridgelet transform of distributions
The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi resolution analysis properties. These relatively new representation systems have encountered wide range…
The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices. We present a self-contained proof of the Fourier transform formula for this distribution. Our method…
We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…
I present a brief update on the transverse polarization distributions, focusing on model calculations and phenomenological perspectives.
In this paper we introduce the notion of a Weinstein two-wavelet. Then we establish and prove the resolution of the identity formula for the Weinstein continuous wavelet transform. Next, we give results on Calder\'on's type reproducing…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
The report deals with classical and quantum descriptions of particles that interact with smooth random potentials, for example ultracold atoms in the dipole potential of an optical speckle pattern. In addition, a discussion of the link…
We are going to study some conditions on which the Radon transform and its dual are invertible. Two function spaces are introduced that the Radon transform on which is bijective linear operator. In this regards, a reconstruction formula is…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from…
A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the…
A review of the present knowledge on polarized parton distributions is given. The effects of perturbative evolution on these distributions are discussed qualitatively and a comparison of various recent parametrizations is made.
We study some of the interactions between the Fourier Transform and the Riemann zeta function (and Dirichlet-Dedekind-Hecke-Tate L-functions)
The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability…
The paper studies various properties of the V-line transform (VLT) in the plane and conical Radon transform (CRT) in $\mathbb{R}^n$. VLT maps a function to a family of its integrals along trajectories made of two rays emanating from a…
In this paper some multidimensional Tauberian theorems for the Lizorkin distributions (without restriction on the support) are proved. Tauberian theorems of this type are connected with the Riesz fractional operators.
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$.