# On Fourier coefficients of some classes of functions and their applications in approximation theory

Commentationes Mathematicae (2014)

- Volume: 54, Issue: 2
- ISSN: 2080-1211

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topE.J. Ibrahimov. "On Fourier coefficients of some classes of functions and their applications in approximation theory." Commentationes Mathematicae 54.2 (2014): null. <http://eudml.org/doc/292544>.

@article{E2014,

abstract = {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.},

author = {E.J. Ibrahimov},

journal = {Commentationes Mathematicae},

keywords = {Fourier-Gegenbauer series; convergence; asymptotic estimation; Gegenbauer transform; strong derivative and of Gegenbauer integral; generalized shift function},

language = {eng},

number = {2},

pages = {null},

title = {On Fourier coefficients of some classes of functions and their applications in approximation theory},

url = {http://eudml.org/doc/292544},

volume = {54},

year = {2014},

}

TY - JOUR

AU - E.J. Ibrahimov

TI - On Fourier coefficients of some classes of functions and their applications in approximation theory

JO - Commentationes Mathematicae

PY - 2014

VL - 54

IS - 2

SP - null

AB - 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.

LA - eng

KW - Fourier-Gegenbauer series; convergence; asymptotic estimation; Gegenbauer transform; strong derivative and of Gegenbauer integral; generalized shift function

UR - http://eudml.org/doc/292544

ER -

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