Related papers: Funk-Minkowski transform and spherical convolution…
We introduce and study deformation $T_{{\bf b},\phi}$ of Minkowski norms in $\mathbb{R}^n$, determined by a set ${\bf b}=(\beta_1,\ldots,\beta_p)$ of linearly independent 1-forms and a smooth positive function $\phi$ of $p$ variables. In…
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several…
In Minkowski geometry the metric features are based on a compact convex body containing the origin in its interior. This body works as a unit ball with its boundary formed by the unit vectors. Using one-homogeneous extension we have a…
Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing…
In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension $n\geq2$ for recovering a smooth function with compact support in the unit ball from spherical means centered on…
The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of…
A convolution representation of continuous translation invariant and SO(n) equivariant Minkowski valuations is established. This is based on a new classification of translation invariant generalized spherical valuations. As applications,…
By adopting the standard definition of diffeomorphisms for a Regge surface we give an exact expression of the Liouville action both for the sphere and the torus topology in the discretized case. The results are obtained in a general way by…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the…
We show that the natural "convolution" on the space of smooth, even, translation-invariant convex valuations on a euclidean space $V$, obtained by intertwining the product and the duality transform of S. Alesker, may be expressed in terms…
In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $\mathbb{S}^d \subset \mathbb{R}^{d+1}$. The reproducing kernel is given by an integral representation using the truncated power function…
The paper is devoted to study the inversion of the integral transform $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,\alpha_i)_{1,p}\\[1mm](b_j,\beta_j)_{1,q}…
We compute non-perturbative spectral functions in a scalar $\phi^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of…
We relate a free scalar field in the Minkowski spacetime with a scalar field with a certain scaling dimension on a sphere of codimension two. This is realised by first performing a Radon transform of the ``bulk" field on the Minkowski space…
In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is…
Tensor Minkowski Functionals (TMFs) are tensorial generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze CMB maps. They encapsulate…
In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…