Strichartz's conjecture for the spinor bundle over the real hyperbolic space

Abstract

Let $H^n(\mathbb{R})$ denote the real hyperbolic space realized as the symmetric space $Spi{n}_0(1,n)/Spin(n)$. In this paper, we provide a characterization for the image of the Poisson transform for $L^2$-sections of the spinor bundle over the boundary ${\partial H}^n(\mathbb{R})$. As a consequence, we obtain an $L^2$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n(\mathbb{R})$, thereby extending Strichartz's conjecture from the scalar case to the spinor setting.

arXiv admin note: text overlap with arXiv:2406.00536