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

摘要

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