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- W2970228796 abstract "For a connected semisimple real Lie group $G$ of non-compact type, Wallach introduced a class of $K$-types called small. We classify all small $K$-types for all simple Lie groups and prove except just one case that each elementary spherical function for each small $K$-type $(pi,V)$ can be expressed as a product of hyperbolic cosines and a Heckman-Opdam hypergeometric function. As an application, the inversion formula for the spherical transform on $Gtimes_K V$ is obtained from Opdam's theory on hypergeometric Fourier transforms." @default.
- W2970228796 created "2019-09-05" @default.
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- W2970228796 date "2019-01-01" @default.
- W2970228796 modified "2023-10-16" @default.
- W2970228796 title "Spherical Functions for Small K-Types" @default.
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- W2970228796 doi "https://doi.org/10.1007/978-3-030-26562-5_6" @default.
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