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On the Orthogonal of a Sum of Periodic Function Spaces

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Abstract

The existence or non-existence of positive orthogonal functions for subspaces of almost periodic functions has important applications in studying the oscillatory behavior of vibrations. Haraux and Komornik have obtained a number of theorems of this type. The purpose of this paper is to answer an open question formulated in the 1980s, and to completely clarify the situation for subspaces defined by three periods.

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Notes

  1. The value \(\ell =-1\) is not used here but we will need it later.

References

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Acknowledgements

The author wants to express his gratitude to Vilmos Komornik for his useful comments and suggestions and Peter Mueller for his help in the proof of Proposition (7.2). He also thanks Mohamad Maassarani for fruitful discussions.

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  1. Département de mathématique, Université de Strasbourg, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Florian Delage

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  1. Florian Delage
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Correspondence to Florian Delage.

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Communicated by Hans G. Feichtinger.

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Delage, F. On the Orthogonal of a Sum of Periodic Function Spaces. J Fourier Anal Appl 24, 1204–1224 (2018). https://doi.org/10.1007/s00041-017-9580-4

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  • DOI: https://doi.org/10.1007/s00041-017-9580-4

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