Single Generator Problem

Junichi Tanaka

Single Generator Problem

Junichi Tanaka^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 H^p(μ), 1 ≤ p ≤ ∞, the corresponding subspaces H_o ^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.

Original language	English
Pages (from-to)	4113-4129
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	348
Issue number	10
Publication status	Published - 1996
Externally published	Yes

Keywords

Cocycles
Ergodic hardy spaces
Outer functions
Single generators

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "Single Generator Problem",

abstract = "Using the Stone-{\v C}ech 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.",

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author = "Junichi Tanaka",

year = "1996",

language = "English",

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journal = "Transactions of the American Mathematical Society",

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T1 - Single Generator Problem

AU - Tanaka, Junichi

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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

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 10

ER -

Single Generator Problem

Abstract

Keywords

ASJC Scopus subject areas

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