Random ergodic sequences on LCA groups

The dimension of ergodic random sequences

Let μ be a computable ergodic shift-invariant measure over {0, 1} . Providing a constructive proof of Shannon-McMillan-Breiman theorem, V’yugin proved that if x ∈ {0, 1} is Martin-Löf random w.r.t. μ then the strong effective dimension Dim(x) of x equals the entropy of μ. Whether its effective dimension dim(x) also equals the entropy was left as an problem question. In this paper we settle this...

Ergodic Theorems on Amenable Groups

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

Ergodic Theorems on Amenable Groups

On T-Pure and Almost Pure Exact Sequences of LCA Groups

A proper short exact sequence 0! A!f B! C ! 0 ð*Þ in the category of locally compact abelian groups is said to be t-pure if fðAÞ is a topologically pure subgroup of B, that is, if

φ-factorable operators and Weyl-Heisenberg frames on LCA groups