On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

Krasniqi, Xhevat Z.. "On the Mixed Modulus of Smoothness and a Class of Double Fourier Series." Mathematica Balkanica New Series 27.1-2 (2013): 53-64. <http://eudml.org/doc/281364>.

@article{Krasniqi2013,
abstract = {MSC 2010: 42A32; 42A20In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.},
author = {Krasniqi, Xhevat Z.},
journal = {Mathematica Balkanica New Series},
keywords = {double Fourier series; modulus of smoothness; Fejer's kernel; mixed modulus of smoothness; Fejér kernel},
language = {eng},
number = {1-2},
pages = {53-64},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {On the Mixed Modulus of Smoothness and a Class of Double Fourier Series},
url = {http://eudml.org/doc/281364},
volume = {27},
year = {2013},
}

TY - JOUR
AU - Krasniqi, Xhevat Z.
TI - On the Mixed Modulus of Smoothness and a Class of Double Fourier Series
JO - Mathematica Balkanica New Series
PY - 2013
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 27
IS - 1-2
SP - 53
EP - 64
AB - MSC 2010: 42A32; 42A20In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.
LA - eng
KW - double Fourier series; modulus of smoothness; Fejer's kernel; mixed modulus of smoothness; Fejér kernel
UR - http://eudml.org/doc/281364
ER -