A characterization of the L²-range of the generalized spectral projections related to the Hodge-de Rham Laplacian

2024/06/01 by Abdelhamid Boussejra, Boussejra, Abdelhamid, Khalid Koufany +1
Mathematics · #43A85 #43A90 #58J50 #Advanced Harmonic Analysis Research #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.00536

openalex publication_date 2024/06/01 · openalex created_date 2024/06/06 · openalex updated_date 2026/08/04

Abstract

Let Hⁿ(\mathbb R) be the real hyperbolic space. In this paper, we present a characterization of the L²-range of the generalized spectral projections on the bundle of differential forms over Hⁿ(\mathbb R). As an underlying result we show a characterization of the L²-range of the Poisson transform on the bundle of differential forms on the boundary ∂ Hⁿ(\mathbb R). This gives a positive answer to a conjecture of Strichartz on differential forms.

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