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 ...

The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral representations are analogs of those previously obtained by S. Agmon, S. Helgason, and other authors for solutions of the Helmholtz equation (i.e., for generalized eigenfu...

This paper presents and discusses data on vowel devoicing in English from Ph.D. research being carried out under Sarah Hawkins at Cambridge, and more recently with Klaus Kohler at the Institut für Phonetik und digitale Sprachverarbeitung in Kiel; and data on vowel deletion in German from the Kiel Corpus of Spontaneous Speech (IPDS 1995, 1996) reported most recently by Pétur Helgason and Klaus K...

Let G be a simple non-compact linear Lie group. ? any irreducible unitary representation of with infinitesimal character ? whose continuous part is ?. The beautiful Helgason-Jonson bound in 1969 says that the norm ? upper bounded by ?(G), which stands for half sum positive roots G. current paper aims to give framework sharpen Helgason—Johnson when infinite-dimensional. We have explicit results ...

The connections between the objects mentioned in the title are used to give a short proof of the Cartan–Helgason theorem and a natural construction of the compactifications.

By further sharpening the Helgason-Johnson bound in 1969, this paper classifies all irreducible unitary representations with non-zero Dirac cohomology of Hermitian symmetric real form E7(−25).

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.

We formulate and prove a Paley-Wiener theorem for Harish-Chandra modules real reductive group. As corollary we obtain new elementary proof of the Helgason conjecture.