On the Translates of Powers of a Continuous Periodic Function

R. A. Kerman; Yitzhak Weit

doi:10.1007/s00041-010-9139-0

On the Translates of Powers of a Continuous Periodic Function

R. A. Kerman, Yitzhak Weit

Department of Mathematics

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

Abstract

We characterize the set of real-valued, 2π-periodic, continuous functions f for which the translation invariant subspace V (f) generated by fⁿ, n ≥ 0, is dense in C (T). In particular, it follows that if f takes a given value at only one point then V (f) is dense in C (T).

Original language	English
Pages (from-to)	786-790
Number of pages	5
Journal	Journal of Fourier Analysis and Applications
Volume	16
Issue number	5
DOIs	https://doi.org/10.1007/s00041-010-9139-0
State	Published - 2010

Keywords

Mean-periodic
Translation invariant

ASJC Scopus subject areas

Analysis
General Mathematics
Applied Mathematics

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10.1007/s00041-010-9139-0

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abstract = "We characterize the set of real-valued, 2π-periodic, continuous functions f for which the translation invariant subspace V (f) generated by fn, n ≥ 0, is dense in C (T). In particular, it follows that if f takes a given value at only one point then V (f) is dense in C (T).",

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AU - Weit, Yitzhak

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AB - We characterize the set of real-valued, 2π-periodic, continuous functions f for which the translation invariant subspace V (f) generated by fn, n ≥ 0, is dense in C (T). In particular, it follows that if f takes a given value at only one point then V (f) is dense in C (T).

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KW - Translation invariant

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M3 - Article

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JO - Journal of Fourier Analysis and Applications

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On the Translates of Powers of a Continuous Periodic Function

Abstract

Keywords

ASJC Scopus subject areas

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