TY - JOUR
T1 - Single Generator Problem
AU - Tanaka, Junichi
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
KW - Cocycles
KW - Ergodic hardy spaces
KW - Outer functions
KW - Single generators
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M3 - Article
AN - SCOPUS:33645944061
SN - 0002-9947
VL - 348
SP - 4113
EP - 4129
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 10
ER -