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Abstract

We prove a trigonometric inequality of Ingham’s type for nonharmonic Fourier series when the gap condition between frequencies does not hold any more.

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References

  1. Ball, J.M. and Slemrod, M.S. (1979). Nonharmonic Fourier series and the stabilization of distributed semilinear control systems.Comm. in Pure and App. Math., 37, 555–587.

    Article  MathSciNet  Google Scholar 

  2. Duffin, R.J. and Schaeffer, A.C. (1952). A class of nonharmonic Fourier series.Trans. Am. Math. Soc., 44, 141–154.

    MathSciNet  Google Scholar 

  3. Haraux, A., Quelques méthods et résultats récents en théorie de la contrôlabilité exacte. Preprint.

  4. Hrushev, S.V., Nikol’skii N.K. and Pavlov, B.S. Unconditional bases of exponentials and reproducing kernels, inComplex Analysis and Spectral Theory, Lecture Notes in Math, 864, 214–335.

  5. Ingham, A.E. (1936). Some trigonometrical inequalities with applications to the theory of series.Math. Zeischrift, 41, 367–379.

    Article  MATH  MathSciNet  Google Scholar 

  6. Jaffard, S., Tucsnak, M. and Zuazua, E. (1997). Singular internal stabilization of the wave equation. To appear in the Journal of Differential Equations.

  7. Kahane, J.P. (1962). Pseudo-périodicité et series de Fourier lacunaires.Annales scientifiques de l’E.N.S.T., 76.

  8. Nürnberger, G. (1989).Approximation by Spline Functions. Springer Verlag, New York.

    MATH  Google Scholar 

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Partially supported by grants PB93-1203 of the DGICYT (Spain) and CHRX-CT94-04771 of the UE.

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Jaffard, S., Tucsnak, M. & Zuazua, E. On a theorem of Ingham. The Journal of Fourier Analysis and Applications 3, 577–582 (1997). https://doi.org/10.1007/BF02648885

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  • DOI: https://doi.org/10.1007/BF02648885

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