Related papers: Radon Transform: Dual Pairs and Irreducible Repres…
Harmonic maps from $\BR^2$ or one-connected domain ${\O}\subset \BR^2$ into $GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the B\"acklund-Darboux transformation is applied to the case of the harmonic maps. A new general formula on…
In this manuscript, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon…
In this paper we study intertwining functors (Radon transforms) for twisted D-modules on partial flag varieties and their relation to the representations of semisimple Lie algebras. We show that certain intertwining functors give…
We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
We consider weighted ray-transforms $P\_W$ (weighted Radon transforms along straight lines) in $\mathbb{R}^d, \, d\geq 2,$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space…
We present a unified approach to the study of Radon transforms related to symmetric groups and to general linear groups GL(n,q) regarded as q-analogues of the former. In both cases, we define a sequence of generalized Radon transforms which…
A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…
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…
Holographic duality conjecture has been proposed to be a novel non-perturbative theoretical framework for the description of strongly correlated electrons. However, the duality transformation is not specified to cause ambiguity in the…
A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A : V \to V$ and $A^* : V \to V$ that satisfy (i) and (ii) below: (i) There exists a basis for…
This article presents extensions of the Cram{\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions…
In Part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations -- which relate some cohomology of the moduli space of…
In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding…
A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld…
Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem…
The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…
Let \(X=G/K\) be a noncompact complex Grassmann manifold of rank \(r\). Let \(\tau_l\) be a character of \(K\), \(G\times_P{\C}\) and \(G\times_K{\C}\) the homogeneous line bundles associated with the representations…