Harmonic Analysis Associated with the Multivariate Laguerre Function

Abstract

In this paper, the generalized Laguerre hypergroup $$\mathbb {K}=[0,+\infty [^{n}\times \mathbb {R}$$ is introduced via the multivariate Laguerre function. The inversion theorem, the Plancherel theorem and a Paley–Wiener-type theorem are established for the generalized Fourier–Laguerre transform.