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Spectra of L1-convolution operators acting on Lp-spaces of commutative hypergroups.

Math. Proc. Camb. Phil. Soc. 151, 503-519 (2011)
Verlagsversion DOI
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter polynomial hypergroups
ISSN (print) / ISBN 0008-1981
e-ISSN 1469-8064
Quellenangaben Band: 151, Heft: 3, Seiten: 503-519 Artikelnummer: , Supplement: ,
Verlag Cambridge Univ. Press
Begutachtungsstatus Peer reviewed