相关论文: Spherical Spectral Synthesis and Two-Radius Theore…

We derive bilateral estimates for the constants appearing in the Fourier transform restricted theorems on the Euclidean sphere for the ordinary and especially radial functions belonging to the Lebesgue-Riesz spaces as well as belonging to…

Spectral synthesis calculations based on three-dimensional stellar atmosphere models are limited by the affordable angular resolution of the radiation field. This hampers an accurate treatment of rotational line broadening. We aim to find a…

We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac…

Spherically symmetrical reductions of self-dual Yang-Mills and Einstein-Plebanski equations are constructed at the same manner. As in the first case we come back to known before solutions (under such kind of reduction but in some different…

Current observations stimulate the production of fully three-dimensional explosion models, which in turn motivates three-dimensional spectrum synthesis for supernova atmospheres. We briefly discuss techniques adapted to address the latter…

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…

We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.

We propose an analytical scattering theory in spectral domain to model the electromagnetic (EM) fields of a gyrotropic sphere in terms of the eigen-functions and their associated spectral eigenvalues/coefficients in a recursive integral…

We introduce nonparaxial spatially accelerating waves whose two-dimensional transverse profiles propagate along semicircular trajectories while approximately preserving their shape. We derive these waves by considering imaginary…

Electrodynamic spherical harmonic is a second rank tensor in three-dimensional space. It allows to separate the radial and angle variables in vector solutions of Maxwell's equations. Using the orthonormalization for electrodynamic spherical…

In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami…

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

We introduce a "radial" two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies…

We show that spectral synthesis thresholds are governed by a quantitative spectral complexity parameter, the Fourier Ratio, in addition to the geometric size of the Fourier support. In the Euclidean setting, we prove that if a compactly…

We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice…

We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…

In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. Using a suitable short range approximation within the formalism of functional…

In the previous paper [25], Stolarsky's invariance principle, known for point distributions on the Euclidean spheres [27], has been extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane.…

The resolution of a conventional telescope used to image visible-light synchrotron radiation is often limited by diffraction effects. To improve resolution, the double-slit interferometer method was developed at KEK and has since become…

We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these…