In this survey several papers related to the Radon transform appeared after 2013 are discussed. For the short survey of the …rst 100 years of the history of the theory, I refer to historical notes in the books of Helgason [7] Natterer [5] and in [50]. Pioneering papers of A. Cormack 1963-64 on "Representation of a function by its line integrals" were devoted to medical applications [3]. Few yea...

in this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...

My interest in this general subject started in 1981 when I had a telephone call from Iceland from a doctor there who had worked with me in the Aberdeen Diabetic Clinic for 1.5 years. Since returning to Iceland, where he was responsible for the Diabetic Service he had completed a meticulous survey of all the insulin-dependent patients in the population of just under 0.25 million people. On analy...

The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and other authors for solutions of the Helmholtz equation. When one restricts the class of solutions further, requiring their growth to be polynomial, one arriv...

This work introduces and characterizes a fast parameterless filter based on the Helgason-Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in the Radon domain, extrapolates intermediate projections between those existing. The resulting sinogram, doubled in views, is then reconstructed by a standard ...

Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on Ring Theory and Commutative ...