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Note on a Result of Kerman and Weit

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Abstract

A result in Kerman and Weit (J. Fourier Anal. Appl. 16:786–790, 2010) states that a real valued continuous function f on the unit circle and its nonnegative integral powers can generate a dense translation invariant subspace in the space of all continuous functions on the unit circle if f has a unique maximum or a unique minimum. In this note we endeavour to show that this is quite a general phenomenon in harmonic analysis.

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Acknowledgements

Authors are thankful to S.C. Bagchi for commenting on an earlier draft. Authors are also thankful to an unknown referee for some suggestions. This work is partially supported by a research grant (No. 2/48(6)/2010-R & DII/10807) of NBHM, India.

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Authors and Affiliations

  1. Department of Math. and Stat., Indian Institute of Technology, Kanpur, 208016, India

    Swagato K. Ray

  2. Stat-Math Unit, Indian Statistical Institute, 203 B. T. Rd., Calcutta, 700108, India

    Rudra P. Sarkar

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  1. Swagato K. Ray
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  2. Rudra P. Sarkar
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Correspondence to Rudra P. Sarkar.

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Communicated by Hans G. Feichtinger.

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Ray, S.K., Sarkar, R.P. Note on a Result of Kerman and Weit. J Fourier Anal Appl 18, 583–591 (2012). https://doi.org/10.1007/s00041-011-9215-0

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  • DOI: https://doi.org/10.1007/s00041-011-9215-0

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