On the Translates of Powers of a Continuous Periodic Function

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On the Translates of Powers of a Continuous Periodic Function

Kerman, R. A.; Weit, Yitzhak

The Journal of fourier analysis and applications, 10/2010, Volume: 16, Issue: 5

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

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