相关论文: Wavelet transform and Radon transform on the Quate…
We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial…
Holomorphic quaternion functions only admit affine functions; thus, the M\"obius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only comprises similarity transformations. We determine a…
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…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general…
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…
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of…
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.
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of…
We apply the Fourier transform technique and a modified version of E. Stein's interpolation theorem communicated by L. Grafakos, to obtain sharp $L^p$-$L^q$ estimates for the Radon transform and more general convolution-type fractional…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and with a connection for a trivial GL(n,C) bundle over that manifold. To each light ray on the manifold we assign the data of paralel transport along that light ray. It…
In their proof of the Drinfeld-Langlands correspondence, Frenkel, Gaitsgory and Vilonen make use of a geometric Fourier transformation. Therefore, they work either with l-adic sheaves in characteristic p>0, or with D-modules in…
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…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
We consider a one-dimensional Radon transform on the group SO(3) which is motivated by texture goniometry. In particular we will derive several inversion formulae and compare them with the inversion of the one-dimensional spherical Radon…
We study higher-rank Radon transforms that take functions on $j$-dimensional totally geodesic submanifolds in the $n$-dimensional real constant curvature space to functions on similar submanifolds of dimension $k >j$. The corresponding dual…