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 ...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/mfms/notes 2013-14/13 1 cont afc spec.pdf] 1. Pseudo-Eisenstein series adjunction to constant term 2. Decomposition of pseudo-Eisenstein series: beginning 3. Eisenstein series 4. Decomposition of pseudo-Eisenstein series: conclusion 5. Plancherel theorem We prove that the ort...

Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the RieszThorin interpolation theorem we get the corresponding results in Lp(R+), 1 ≤ p ≤ 2 for the Kontorovich-Lebedev, Mehler-Fock and Olevskii index transforms. An inversion theorem is proved for general index transformat...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...