Geodesic
Uniform convergence of double trigonometric series
Mathematica Bohemica, Tome 138 (2013) no. 3, pp. 225-243.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2013.143434
Classification : 42A20, 42A32, 42B99
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 
@article{10_21136_MB_2013_143434,
     author = {K\'orus, P\'eter},
     title = {Uniform convergence of double trigonometric series},
     journal = {Mathematica Bohemica},
     pages = {225--243},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2013},
     doi = {10.21136/MB.2013.143434},
     mrnumber = {3136495},
     zbl = {06260031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143434/}
}
TY  - JOUR
AU  - Kórus, Péter
TI  - Uniform convergence of double trigonometric series
JO  - Mathematica Bohemica
PY  - 2013
SP  - 225
EP  - 243
VL  - 138
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143434/
DO  - 10.21136/MB.2013.143434
LA  - en
ID  - 10_21136_MB_2013_143434
ER  - 
%0 Journal Article
%A Kórus, Péter
%T Uniform convergence of double trigonometric series
%J Mathematica Bohemica
%D 2013
%P 225-243
%V 138
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143434/
%R 10.21136/MB.2013.143434
%G en
%F 10_21136_MB_2013_143434
Kórus, Péter. Uniform convergence of double trigonometric series. Mathematica Bohemica, Tome 138 (2013) no. 3, pp. 225-243. doi : 10.21136/MB.2013.143434. http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143434/

Cité par Sources :