Spherical analysis on the $(2n+2)$-dimensional oscillator group

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发表日期：

2024年3月21日

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Walid Amghar,
Said Fahlaoui

摘要

In this paper, we present the $(2n+2)$ $(2 n + 2)$ -dimensional oscillator group $G_n(\gamma )$ $G_{n} (γ)$ and its unitary irreducible representations using the Mackey theory. We define the Fourier transform and prove the inversion formula. Additionally, we introduce various Gelfand pairs on $G_n(\gamma )$ $G_{n} (γ)$ and determine the bounded spherical functions associated with these pairs. We provide their expressions using representations and present several properties of the spherical Fourier transform on the oscillator group.

Spherical analysis on the \((2n+2)\)-dimensional oscillator group

摘要