9,868 research outputs found
A survey on spectral multiplicities of ergodic actions
Given a transformation of a standard measure space , let \Cal
M(T) denote the set of spectral multiplicities of the Koopman operator
defined in by . It is discussed in
this survey paper which subsets of are realizable as
\Cal M(T) for various : ergodic, weakly mixing, mixing, Gaussian, Poisson,
ergodic infinite measure preserving, etc. The corresponding constructions are
considered in detail. Generalizations to actions of Abelian locally compact
second countable groups are also discussed
- …