einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue’s integrable complexvalued function f on T, Pγ [f ] is a complex-valued harmonic function in D and it coincides with the classical...

We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The a(x,η) are elements C * S 1, classes that have limited regularity in the x variable. show associated operator a(x, D) maps between Sobolev ℌ FIO (ℝn) and over space (ℝn). Our main result implies m = 0, δ =l/2 r > n − acts boundedly all p ∈ (1, ∞).

In this paper we establish a relation between the support of a function f on Ω1 ⊂ R with differentiability properties of its image Tf on Ω2 ⊂ R under a linear operator T . The classical approach requires analytic continuation of the image Tf from Ω2 into the complex domain C (theorems of Paley-Wiener type [5, 6, 7]), and therefore, could not apply to functions whose images Tf are not analytic a...

The aim of this paper is to prove new uncertainty principles for an integral operator T with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function f ∈ L(R, μ) is highly localized near a single point then T (f) cannot be concentrated in a set of finite measure. The second...

In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X, g) which are de Sitterlike at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X ...

In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X, g) which are de Sitterlike at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X ...

Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moment’s discretization to the hypersingular volume integral equation in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green’s function and the contrast source over the domain of interest. For electrically l...

We introduce a fast algorithm for computing volume potentials that is, the convolution of a translation invariant, free-space Green’s function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Green’s function by cutting off the interaction in physical space beyond the domain of interest. This permits the ...

In this paper we present an electric field volume integral equation approach to simulate surface plasmon propagation along metal/dielectric interfaces. Metallic objects embedded in homogeneous dielectric media are considered. Starting point is a so-called weak-form of the electric field integral equation. This form is discretized on a uniform tensorproduct grid resulting in a system matrix whos...