Distant future and analytic measures

Junichi Tanaka

doi:10.1090/S0002-9947-1986-0846607-6

Distant future and analytic measures

Junichi Tanaka^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Using a representation of analytic measures in terms of a flow built under a function, it is shown that a positive measure is the total variation measure of an analytic measure if and only if the distant future is the zero subspace. This settles a problem posed by Forelli in connection with his generalization of F. and M. Riesz theorems. We also provide another version of Helson’s existence theorem.

Original language	English
Pages (from-to)	799-814
Number of pages	16
Journal	Transactions of the American Mathematical Society
Volume	296
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1986-0846607-6
Publication status	Published - 1986
Externally published	Yes

Keywords

Analytic measures
Distant future
Quasi-invariant measures

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1986-0846607-6

Cite this

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title = "Distant future and analytic measures",

abstract = "Using a representation of analytic measures in terms of a flow built under a function, it is shown that a positive measure is the total variation measure of an analytic measure if and only if the distant future is the zero subspace. This settles a problem posed by Forelli in connection with his generalization of F. and M. Riesz theorems. We also provide another version of Helson{\textquoteright}s existence theorem.",

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AB - Using a representation of analytic measures in terms of a flow built under a function, it is shown that a positive measure is the total variation measure of an analytic measure if and only if the distant future is the zero subspace. This settles a problem posed by Forelli in connection with his generalization of F. and M. Riesz theorems. We also provide another version of Helson’s existence theorem.

KW - Analytic measures

KW - Distant future

KW - Quasi-invariant measures

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Distant future and analytic measures

Abstract

Keywords

ASJC Scopus subject areas

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