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 ...

We prove two versions of Beurling’s theorem for Riemannian symmetric spaces of arbitrary rank. One of them uses the group Fourier transform and the other uses the Helgason Fourier transform. This is the master theorem in the quantitative uncertainty principle.

the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan's theorem.

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

In this paper we extend classical Titchmarsh theorems on the Fourier–Helgason transform of Lipschitz functions to setting L p -space Damek–Ricci spaces. As consequences, quantitative Riemann–Lebesgue estimates are obtained and an integrability result for is developed extending ideas used by in one dimensional setting.

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.