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Real analytic expansion of spectral projections and extension of the Hecke-Bochner identity

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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 × φ n−1 k for function f ∈ L p(ℂn) with 1 ≤ p ≤ ∞. 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 × φ n−1 k for function f ∈ L 2(ℂn). Using this expansion we deduce that a complex cone can be a set of injectivity for the twisted spherical means.

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Authors and Affiliations

  1. School of Mathematics, Harish-Chandra Research Institute, Allahabad, India, 211019

    Rajesh K. Srivastava

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  1. Rajesh K. Srivastava
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Correspondence to Rajesh K. Srivastava.

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Srivastava, R.K. Real analytic expansion of spectral projections and extension of the Hecke-Bochner identity. Isr. J. Math. 200, 171–192 (2014). https://doi.org/10.1007/s11856-014-1041-z

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  • DOI: https://doi.org/10.1007/s11856-014-1041-z

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