Geodesic
Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $
Colloquium Mathematicum, Tome 65 (1993) no. 1, pp. 103-116.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study polyhedral Dirichlet kernels on the n-dimensional torus and we write a fairly simple formula which extends the one-dimensional identity $∑_{j=-N}^N e^{ijt} = sin((N+(1/2))t) / sin((1/2)t)$. We prove sharp results for the Lebesgue constants and for the pointwise boundedness of polyhedral Dirichlet kernels; we apply our results and methods to approximation theory, to more general summability methods and to Fourier series on compact Lie groups, where we write an asymptotic formula for the Dirichlet kernels.
DOI : 10.4064/cm-65-1-103-116
Keywords: Fourier series on compact Lie groups, Lebesgue constants, polyhedral Dirichlet kernels, multiple Fourier series

Giancarlo Travaglini 1

1 
@article{10_4064_cm_65_1_103_116,
     author = {Giancarlo Travaglini},
     title = {Polyhedral summability of multiple {Fourier} series (and explicit formulas for {Dirichlet} kernels on $},
     journal = {Colloquium Mathematicum},
     pages = {103--116},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {1993},
     doi = {10.4064/cm-65-1-103-116},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-65-1-103-116/}
}
TY  - JOUR
AU  - Giancarlo Travaglini
TI  - Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $
JO  - Colloquium Mathematicum
PY  - 1993
SP  - 103
EP  - 116
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-65-1-103-116/
DO  - 10.4064/cm-65-1-103-116
LA  - en
ID  - 10_4064_cm_65_1_103_116
ER  - 
%0 Journal Article
%A Giancarlo Travaglini
%T Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $
%J Colloquium Mathematicum
%D 1993
%P 103-116
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-65-1-103-116/
%R 10.4064/cm-65-1-103-116
%G en
%F 10_4064_cm_65_1_103_116
Giancarlo Travaglini. Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $. Colloquium Mathematicum, Tome 65 (1993) no. 1, pp. 103-116. doi : 10.4064/cm-65-1-103-116. http://geodesic.mathdoc.fr/articles/10.4064/cm-65-1-103-116/

Cité par Sources :