Abstract
The classical Hecke identity gives the Fourier transform of the product of a homogeneous harmonic polynomial h times the Gaussian e−1/2<...>. A similar formula is valid when the Gaussian is replaced by the tempered distribution ei/2<...>. It is shown that there is a similar identity when the inner product is replaced by an indefinite quadratic formq and h is a Л-harmonic distribution, where Л is the differential operator canonically associated toq. Another generalization is obtained in the context of representations of Jordan algebras, in the spirit of Herz's previous work on matrix spaces.
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Communicated by Robert Strichartz
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Clerc, JL. A generalized hecke identity. The Journal of Fourier Analysis and Applications 6, 105–111 (2000). https://doi.org/10.1007/BF02510121
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DOI: https://doi.org/10.1007/BF02510121