Related papers: Symplectic Radon Transform and the Metaplectic Rep…
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literature. Some of these are recalled in the Introduction. In this…
Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…
In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
An effective model for describing the relativistic quantum dynamics of a radiating electron is developed via a relativistic generalization of the Lindblad master equation. By incorporating both radiation reaction and vacuum fluctuations…
Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on $R^n$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp…
In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated…
We consider the Radon transform associated to dual pairs $(X,\Xi)$ in the sense of Helgason, with $X=G/K$ and $\Xi=G/H$, where $G=\mathbb{R}^d\rtimes K$, $K$ is a closed subgroup of ${\rm GL}(d,\mathbb{R})$ and $H$ is a closed subgroup of…
Let $G$ be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of G, we determine its Langlands parameter (equivalently, its Jordan blocks…
The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of…
The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
This note contains a short proof of a classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices.
In this article we study the spherical mean Radon transform in $\mathbf R^3$ with detectors centered on a plane. We use the consistency method suggested by the author of this article for the inversion of the transform in 3D. A new iterative…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
This paper explores possibilities for new uses of the Radon transform for imaging and analysis of lightfields. We show that the previously reported Dimansionality Gap can be derived from an ultrahyperbolic PDE, first proposed by F. John,…