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

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

2012-04-13

arxiv.org/abs/1204.3076v2

Mathematics

Functional Analysis

15 pages. arXiv admin note: text overlap with arXiv:1103.4571

Scientific paper

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 $f\times\varphi_k^{n-1}$ for function $f\in L^p(\mathbb C^n)$ with $1\leq p\leq\infty.$ Then, we derive a real analytic expansion for the spectral projections $f\times\varphi_k^{n-1}$'s for the function $f\in L^2(\mathbb C^n).$

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