The trace class conjecture without the K-finiteness assumption |
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| Institution: | 1. National Research Council, Institute of Science and Technology for Ceramics, Via Granarolo 64, 48018, Faenza, Italy;2. Institute of Structures and Design, German Aerospace Center, Pfaffenwaldring 38-40, 70569, Stuttgart, Germany;1. Key Laboratory for the Green Preparation and Application of Functional Materials Ministry of Education, Hubei Key Laboratory of Polymer Materials, School of Materials Science and Engineering, Hubei University, Wuhan, 430062, People''s Republic of China;2. Hubei Nuclear Solid Physics Key Laboratory, Department of Physics, Wuhan University, Wuhan, 430072, People''s Republic of China;1. College of Chemistry and Molecular Sciences, Hubei Engineering Center of Natural Polymer-based Medical Materials, Key Laboratory of Biomedical Polymers of Ministry of Education, Wuhan University, Wuhan, 430072, China;2. Zhongnan Hospital of Wuhan University, Wuhan, Hubei, 430071, China;1. Biomaterial Research Laboratory, Department of Material Science and Engineering, College of Chemistry and Materials, Jinan University, Guangzhou, 510632, PR China;2. Engineering Research Center of Artificial Organs and Materials, Ministry of Education, Guangzhou, 510632, PR China |
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| Abstract: | Let G be the group of real points of a reductive algebraic ?-group satisfying the same assumptions as in 5], Chapter I, and let Γ be a discrete subgroup of G. Let RΓ be the right regular representation of G in L2(Γ\G). We prove in this Note that, for any integrable rapidly decreasing function ? on G, the restriction of RΓ(?) to the discrete spectrum of RΓ is a trace class operator. |
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