### A dimension group for local homeomorphisms and endomorphisms of onesided shifts fo finite type.

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Given an arbitrary countable subgroup ${\sigma}_{0}$ of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to ${\sigma}_{0}$. For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

Let $(Z,{T}_{Z})$ be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of $(Z,{T}_{Z})$ is Borel isomorphic to an almost 1-1 extension of $(Z,{T}_{Z})$. Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz...

The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ${}^{\omega}$, the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form $({a}_{p},s)={\prod}_{p}{(1-{a}_{p}{p}^{-s})}^{-1}$ for ${a}_{p}$ in ${}^{\omega}$. Among other things, using the Haar measure on ${}^{\omega}$ for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.