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

E.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 -