Sharp estimates for the convergence rate of Fourier—Bessel series

Sharp estimates for the convergence rate of Fourier—Bessel series

Sharp estimates are derived for the convergence rate of Fourier series in terms of Bessel functions of the first kind for some classes of functions characterized by a generalized modulus of continuity. The Kolmogorov N -width of these classes of functions are also estimated.

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Veröffentlicht in:Computational mathematics and mathematical physics 2015-06, Vol.55 (6), p.907-916
Hauptverfasser: Abilov, V. A., Abilova, F. V., Kerimov, M. K.
Format: Artikel
Sprache:eng
Schlagworte:
Bessel functions
Computational mathematics
Computational Mathematics and Numerical Analysis
Continuity
Convergence
Estimates
Estimating techniques
Fourier analysis
Fourier series
Fourier-Bessel transformations
Mathematical analysis
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Physics
Studies
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Beschreibung
Zusammenfassung:Sharp estimates are derived for the convergence rate of Fourier series in terms of Bessel functions of the first kind for some classes of functions characterized by a generalized modulus of continuity. The Kolmogorov N -width of these classes of functions are also estimated.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542515060020