Distant future and analytic measures

Tanaka, Jun-ichi

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

Distant future and analytic measures
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Trans. Amer. Math. Soc. 296 (1986), 799-814 Request permission

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.

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Fourier theory and flows

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