A note on the L²-harmonic analysis of the Joint-Eigenspace Fourier transform

2024/10/03 by Olufemi O. Oyadare, Oyadare, O. O.
Computer Science · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods

paper · pdf · doi:10.48550/arxiv.2410.09075

openalex publication_date 2024/10/03 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

Abstract

We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group G on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on its corresponding symmetric space G/K. The L²-decomposition of the Joint-Eigenspace Fourier transform leads to the complete characterization of the said irreducibility in terms of the simplicity of a pair of members of \mathfraka^*_ℂ.

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