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Annihilating properties of convolution operators on complex spheres

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This paper studies annihilating properties of operators generated by spherical convolution over the unit sphere Ω2q of Cq. Its specific aim is to answer the following question: given a complex number γ, |γ|≤1, to determine what functions of L2(Ω2q) have zero average over every section  Ω w γ,q  :={ z ∈Ω2q: <z,w> = γ} of Ω2q . Here, <.,.>stands for the usual inner product of Cq.

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Authors and Affiliations

  1. Departamento de Matemática, ICMC-USP, São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brasil

    V. A. Menegatto

  2. Universidade Federal de Itajubá, ICI-DMC, Caixa Postal 50, 37500-903 Itajubá MG, Brasil

    C. P. Oliveira

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  1. V. A. Menegatto
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  2. C. P. Oliveira
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Menegatto, V., Oliveira, C. Annihilating properties of convolution operators on complex spheres. Anal Math 31, 13–30 (2005). https://doi.org/10.1007/s10476-005-0002-5

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  • DOI: https://doi.org/10.1007/s10476-005-0002-5

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