Spectra of L<sup>1</sup>-convolution operators acting on <em>L</em><sup>p</sup>-spaces of commutative hypergroups.
- Perreiter, E.
DOIAbstract
We show that, for commutative hypergroups, the spectrum of all L1-convolution operators on Lp is independent of p ∈ [1, ∞] exactly when the Plancherel measure is supported on the whole character space χb(K), i.e., exactly when L1(K) is symmetric and for every α ∈ Reiter's condition P2 holds true. Furthermore, we explicitly determine the spectra σp(Tϵ1) for the family of Karlin-McGregor polynomial hypergroups, which demonstrate that in general the spectra might even be different for each p
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