Related papers: On the Radon transform and the Dirac delta distrib…
We compare the Radon transform in its standard and symplectic formulations and argue that the inversion of the latter can be performed more efficiently.
In this paper we consider the generalized Radon transform $\mathcal R$ in the plane. Let $f$ be a piecewise smooth function, which has a jump across a smooth curve $\mathcal S$. We obtain a formula, which accurately describes view aliasing…
A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities…
In this work, we construct an explicit, theoretically rigorous deconvolution method that relies entirely on iterative forward convolutions, thus can be numerically implemented. We first prove that convolution with an even Schwartz kernel…
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…
Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincar\'{e} space is found. Also, by means of some estimates for hyperbolic…
We show that discrete singular Radon transforms along a certain class of polynomial mappings $P:\mathbb{Z}^d\to \mathbb{Z}^n$ satisfy sparse bounds. For $n=d=1$ we can handle all polynomials. In higher dimensions, we pose restrictions on…
We construct a multiresolution theory for spaces bigger then L^2(R). For a good choice of the dilation and translation operators on these larger spaces, it is possible to build singly generated wavelet bases, thus obtaining examples of…
This work characterizes the range of the single-quadrant approximate discrete Radon transform (ADRT) of square images. The characterization follows from a set of linear constraints on the codomain. We show that for data satisfying these…
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective…
We present theoretical results for superradiance, i.e. the collective coherent decay of a radiating system, in a semiconductor heterostructure under a strong quantizing magnetic field. We predict a strong peak (`Dicke-peak') in the emission…
This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…
We define and study the (minimal) Radon transform on a real symmetric variety.
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…
We consider the Radon transform along lines in an $n$ dimensional vector space over the two element field. It is well known that this transform is injective and highly overdetermined. We classify the minimal collections of lines for which…
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…
We show that Mellin moments of generalized parton distributions, given as even polynomials in the skewness parameter, are obtained from the Taylor expansion of light front wave functions. Furthermore, we derive non-standard versions of the…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
Approximate solutions of the Dirac equation are found for ultrarelativistic particles moving in a periodic potential, which depends only on one coordinate, transverse to the largest component of the momentum of the incoming particle. As an…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…