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arXiv · 2406.00536

A characterization of the $L^2$-range of the generalized spectral projections related to the Hodge-de Rham Laplacian

Abdelhamid Boussejra·Khalid Koufany
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Abstract

Let $H^n(\mathbb R)$ be the real hyperbolic space. In this paper, we present a characterization of the $L^2$-range of the generalized spectral projections on the bundle of differential forms over $H^n(\mathbb R)$. As an underlying result we show a characterization of the $L^2$-range of the Poisson transform on the bundle of differential forms on the boundary $\partial H^n(\mathbb R)$. This gives a positive answer to a conjecture of Strichartz on differential forms.

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Abdelhamid Boussejra, Khalid Koufany. 2024-06-01. A characterization of the $L^2$-range of the generalized spectral projections related to the Hodge-de Rham Laplacian. https://arxiv.org/abs/2406.00536

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