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Approximation of classes of Poisson integrals by incomplete Fejér means

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Abstract

The work is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. One of the important direction in this field is the study of asymptotic behavior of the upper bounds over a fixed classes of periodic functions of deviations of the trigonometric polynomials. In paper asymptotic behavior of the upper bounds over classes of Poisson integrals of periodic functions of the real variable of deviations of linear means of Fourier series, which are defined by applying the Fejér summation method, is studied. The mentioned classes consist of analytic functions of a real variable, which can be regularly extended into the corresponding strip of the complex plane. We solve the problem of finding the asymptotic inequalities for the upper bound of deviations of the incomplete Fejér means in the class of Poisson integrals.

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Acknowledgements

This research is supported by the Volkswagen Foundation project “From Modeling and Analysis to Approximation".

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  1. Department of Theory of Functions, Institute of Mathematics of NAS of Ukraine, Tereschenkivska str. 3, Kyiv, 01601, Ukraine

    Olga Rovenska

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  1. Olga Rovenska
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Correspondence to Olga Rovenska.

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Rovenska, O. Approximation of classes of Poisson integrals by incomplete Fejér means. J Anal 32, 1433–1442 (2024). https://doi.org/10.1007/s41478-023-00692-2

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  • DOI: https://doi.org/10.1007/s41478-023-00692-2

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