Related papers: Trkalian fields and Radon transformation
Non-abelian T duality (NATD) is a symmetry of the worldsheet action that allows one to generate new solutions of string theory by performing algebraic transformations of known geometries. Applications of such transformations to spheres have…
Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…
The notion of the Radon transform on the Heisenberg group was introduced by R. Strichartz and inspired by D. Geller and E.M. Stein's related work. The more general transversal Radon transform integrates functions on the m-dimensional real…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
We obtain sharp norm estimates for fractional integrals generated by Radon transforms of three types in the n-dimensional real Euclidean space. The method relies on recent interpolation results for analytic families of operators.
Motivated by recent work on the Sachdev-Ye-Kitaev (SYK) model, we consider the effect of Radon or X-ray transformations, on the Laplace eigenfunctions in hyperbolic Bolyai-Lobachevsky space. We show that the Radon map from this space to…
For an oscillating electric dipole in the shape of a small, solid, uniformly-polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables…
We study a 6d model of a set of self-dual 2-form $B$-fields interacting with a non-abelian vector $A$-field which is restricted to a 5d subspace. One motivation is that if the gauge vector could be expressed in terms of the $B$-field or…
The sonar transform in geometric tomography maps functions on the Euclidean half-space to integrals of those functions over hemispheres centered on the boundary hyperplane. We obtain sharp $L^p$-$L^q$ estimates for this transform and new…
The aim of this paper is to present inversion methods for the classical Radon transform which is defined on a family of $k$ dimensional planes in $\Bbb R^{n}$ where $1\leq k\leq n - 2$. For these values of $k$ the dimension of the set…
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an $\ell^p$ result for translation invariant discrete singular Radon transforms to a class of twisted operators including…
Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field…
We define the Radon transform functor for sheaves and prove that it is an equivalence after suitable microlocal localizations. As a result, the sheaf category associated to a Legendrian is invariant under the Radon transform. We also manage…
A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It…
We define and study the (minimal) Radon transform on a real symmetric variety.
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.