Geodesic
On Fourier coefficients of some classes of functions and their applications in approximation theory
Commentationes Mathematicae, Tome 54 (2014) no. 2, pp. 209-246.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In the paper, the behavior of Fourier coefficients of some classes of functions on an arbitrary orthogonal system is studied. The estimates of order of convergence to zero of Fourier-Gegenbauer coefficients are found. These estimates are precise and are of terminal character. The obtained results are used in convergence of Fourier-Gegenbauer series.
DOI : 10.14708/cm.v54i2.704
Mots-clés : Fourier-Gegenbauer series, convergence, asymptotic estimation, Gegenbauer transform, strong derivative and of Gegenbauer integral, generalized shift function 
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E.J. Ibrahimov. On Fourier coefficients of some classes of functions and their applications in approximation theory. Commentationes Mathematicae, Tome 54 (2014) no. 2, pp.  209-246. doi : 10.14708/cm.v54i2.704. http://geodesic.mathdoc.fr/articles/10.14708/cm.v54i2.704/

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