Péter Kórus, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1, Hungary, e-mail: korpet@math.u-szeged.hu
Abstract: It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone or general monotone double sequences. In this paper we give new sufficient conditions for the uniformity of the regular convergence of sine-cosine and double cosine series, which are necessary as well in case the coefficients are non-negative. The new results also bring necessary and sufficient conditions for the uniform regular convergence of double trigonometric series in complex form.
Keywords: sine series, cosine series, double sine series, sine-cosine series, double cosine series, uniform convergence, regular convergence, general monotone sequence, general monotone double sequence, supremum bounded variation
Classification (MSC 2010): 42A20, 42A32, 42B99
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
