SPECTRAL MULTIPLICITIES FOR ERGODIC FLOWS

Let E be a subset of positive integers such that E boolean AND {1, 2} not equal empty set. A weakly mixing finite measure preserving flow T = (T-t)(t is an element of R) is constructed such that the set of spectral multiplicities (of the corresponding Koopman unitary representation generated by T) is E. Moreover, for each non-zero t is an element of R, the set of spectral multiplicities of the transformation T-t is also E. These results are partly extended to actions of some other locally compact second countable Abelian groups.