Geodesic
Convergence of Double Fourier Series after a Change of Variable
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 267-277

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove that for any compact set $\Omega\subset C(\mathbb T^2)$ there exists a homeomorphism $\tau$ of the closed interval $\mathbb T=[-\pi,\pi]$ such that for an arbitrary function $f\in\Omega$ the Fourier series of the function $F(x,y)=f(\tau(x),\tau(y))$ converges uniformly on $C(\mathbb T^2)$ simultaneously over rectangles, over spheres, and over triangles. 
@article{MZM_2003_74_2_a8,
     author = {A. A. Sahakian},
     title = {Convergence of {Double} {Fourier} {Series} after a {Change} of {Variable}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {267--277},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/}
}
TY  - JOUR
AU  - A. A. Sahakian
TI  - Convergence of Double Fourier Series after a Change of Variable
JO  - Matematičeskie zametki
PY  - 2003
SP  - 267
EP  - 277
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/
LA  - ru
ID  - MZM_2003_74_2_a8
ER  - 
%0 Journal Article
%A A. A. Sahakian
%T Convergence of Double Fourier Series after a Change of Variable
%J Matematičeskie zametki
%D 2003
%P 267-277
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/
%G ru
%F MZM_2003_74_2_a8
A. A. Sahakian. Convergence of Double Fourier Series after a Change of Variable. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/