On the Selberg Trace Formula in the Case of Compact Quotient
نویسندگان
چکیده
It is a standard fact (see §2) that 7rr(4>) is of trace class. In particular, 7Tr(4>) is completely continuous for 4>eC7(G). This implies that L(r\G) decomposes into an orthogonal direct sum of irreducible invariant subspaces, {HjK°=i and for each i there are only a finite number of k so that H, is equivalent with Hk as a representation of G (cf. Gelfand, Graev, PyateckiïShapiro [9]). Let G denote the set of equivalence classes of irreducible representations of G. Then we have observed that
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