Book Review: Harmonic analysis of spherical functions on real reductive groups
نویسندگان
چکیده
منابع مشابه
Harmonic Analysis on Real Reductive Symmetric Spaces
Let G be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over R. Let σ be an involution of the Lie group G, H an open subgroup of the subgroup of fixed points of σ. One decomposes the elements of L(G/H) with the help of joint eigenfunctions under the algebra of le...
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Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...
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| Two natural deenitions of bi-harmonic functions on countable groups are shown to essentially coincide. Criteria of absence of non-constant bounded bi-harmonic functions are formulated. A description of these functions for free groups is given. Fonctions bi-harmoniques sur les groupes R esum e R esum e | Nous montrons l' equivalence essentielle de deux d eenitions naturelles des fonctions bi-h...
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When Ian Macdonald’s book Spherical functions on a group of p-adic type first appeared, it was one of a very small number of publications concerned with representations of p-adic groups. At just about that time, however, the subject began to bewidely recognized as indispensable in understanding automorphic forms, and the literature on the subject started to grow rapidly. Since it has by now gro...
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is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1990
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1990-15996-8