Real analytic expansion of spectral projection and extension of Hecke-Bochner identity

Abstract

In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times {\phi }_k^{n-1}$ for function $f\in L^p({\mathbb{C}}^n)$ with $1\le p\le \infty .$ We prove that spheres are sets of injectivity for the twisted spherical means with real analytic weight. Then, we derive a real analytic expansion for the spectral projections $f\times {\phi }_k^{n-1}$ for function $f\in L^2({\mathbb{C}}^n).$

arXiv comment18 pages, appeared in Israel J. Math

References in corpus (1)

• Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb{C}$

Cited by in corpus (1)

• Non-harmonic cones are sets of injectivity for the twisted spherical means on ${\mathbb{C}}^n$