Introductory lectures on automorphic forms
نویسنده
چکیده
1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic forms. Even though the material below looks complicated it is just the tip of the iceberg. 1.1 Left invariant measures. Let X be a locally compact topological space with a countable basis for its topology. Let C(X) denote the space of all continuous complex valued functions on X. If f is a function on X then we denote by supp(f) the closure of the set {x ∈ X|f (x) = 0}. We set C c (X) = {f ∈ C(X)|supp(f) is compact}. If K ⊂ X is a compact subset then we set C K (X) = {f ∈ C(X)|supp(f) ⊂ K}. Whe endow each space with the norm topology induced by f K = max x∈K |f (x)|. We endow C c (X) with the union topology. That is, a subbasis of the topology is the set consisting of the sets that are open subsets of some C K (X). With this notation in place a complex measure on X is a continuous linear map µ : C c (X) → C. A measure is a complex measure µ such that µ(f) is real if f is real valued and non-negative if f takes on only non-negative values.
منابع مشابه
Automorphic forms , L - functions and number theory ( March 12 – 16 ) Three Introductory lectures
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