Using the Stone-Čech compactification βZ of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces Hp(μ), 1 ≤ p ≤ ∞, the corresponding subspaces Ho p(μ) are all singly generated. This shows the existence of maximal weak-* Dirichlet algebras, different from H∞ of the disc, for which the single generator problem is settled.
|Number of pages||17|
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1996|
- Ergodic hardy spaces
- Outer functions
- Single generators
ASJC Scopus subject areas