Related papers: Invariant Differential Operators and the Radon Tra…
The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
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…
We study a family $C_{s,l}$ of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The $C_{s,l}$ descend to invariant differential operators on the corresponding Grassmannian,…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
We consider the Radon transform for a dual pair $(X,\Xi)$, where $X=G/K$ is a noncompact symmetric space and $\Xi$ is the space of horocycles of $X$. We address the unitarization problem that was considered (and solved in some cases) by…
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…
The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…
A support theorem for the horocycle Radon transform f \to \hat{f} is a property of the form \hat{f} of compact support \rightarrow f of compact support. Here we prove a variation of this result where support (\hat{f}) is outside a fixed…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…
In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform…
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions…
We study the different horospherical Radon transforms that arise by regarding a homogeneous tree T as a simplicial complex whose simplices are vertices V, edges E or flags F (flags are oriented edges). The ends (infinite geodesic rays…
Let $F$ be a local field and $n\ge 2$ an integer. We study the Radon transform as an operator $M : \mathcal C_+ \to \mathcal C_-$ from the space of smooth $K$-finite functions on $F^n \setminus \{0\}$ with bounded support to the space of…
Let $\mathscr Q$ be the quaternion Heisenberg group, and let $\mathbf P$ be the affine automorphism group of $\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary…
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…
Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any…