The problem of finding the explicit Plancherel formulas for semisimple Lie groups has been solved completely in the case of complex semisimple Lie groups (see [3 (b)]). Moreover Harish-Chandra showed [3(f)] that the problem is solved also for a real semisimple Lie group having only one conjugate class of Cartan subgroups. In the case of real semisimple Lie groups with several conjugate classes ...

The primary purpose of this paper is to show that every valuation on the field of meromorphic functions of bounded type on a finitely sheeted unlimited covering Riemann surface is a point valuation if and only if the same is true on its base Riemann surface. The result is then applied to concrete examples and some related results are obtained. Any valuation on the field M(W) of single valued me...

In the author's paper [l ] it is shown that if a sequence of orientable »-dimensional generalized closed manifolds (abbreviated »-gem) converge (« —1)-regularly to an »-dimensional set, then the limit set is also an orientable »-gem (see Definitions 1 and 2). In this paper a similar result is obtained for manifolds with boundary. Throughout the paper we assume that our sets are imbedded in a co...