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Estimates for exponential sums. Applications

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We obtain estimates of exponential (in particular, trigonometric) sums in terms of rational functions. Examples of sharp inequalities are given. These inequalities are used for estimating solutions to linear homogeneous differential equations with constant coefficients. The main results are based on the estimates of the moduli of the derivatives of rational functions by variable majorants (comparison functions) of a special form. Bibliography: 9 titles.

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Authors and Affiliations

  1. Vladimir State University, 87, ul. Gor’kogo, Vladimir, 600000, Russia

    V. I. Danchenko & A. E. Dodonov

Authors
  1. V. I. Danchenko
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  2. A. E. Dodonov
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Correspondence to V. I. Danchenko.

Additional information

Translated from Problemy Matematicheskogo Analiza 67, November 2012, pp. 23–30.

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Danchenko, V.I., Dodonov, A.E. Estimates for exponential sums. Applications. J Math Sci 188, 197–206 (2013). https://doi.org/10.1007/s10958-012-1118-3

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  • DOI: https://doi.org/10.1007/s10958-012-1118-3

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