Probability measures on compact groups which have square-integrable densities

Probability Measures on Compact Groups which have Square-Integrable Densities

We apply Peter-Weyl theory to obtain necessary and sufficient conditions for a probability measure on a compact group to have a square-integrable density. Applications are given to measures on the d-dimensional torus. MSC 2000: 60B15, 60E07, 43A05, 43A30

Probability on Compact Lie Groups

Densities on locally compact abelian groups

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

ON SQUARE-INTEGRABLE REPRESENTATIONS OF CLASSICAL p-ADIC GROUPS II

In this paper, we continue our study of non-supercuspidal discrete series for the classical groups Sp(2n, F ), SO(2n+ 1, F ), where F is p-adic.

On Square-Integrable Representations of Classical p-adic Groups

In this paper, we use Jacquet module methods to study the problem of classifying discrete series for the classical p-adic groups Sp(2n, F) and SO(2n + 1, F).