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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.
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 -