Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $
Colloquium Mathematicum, Tome 65 (1993) no. 1, pp. 103-116
Cet article a éte moissonné depuis 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.
Keywords:
Fourier series on compact Lie groups, Lebesgue constants, polyhedral Dirichlet kernels, multiple Fourier series
Affiliations des auteurs :
Giancarlo Travaglini 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},
year = {1993},
volume = {65},
number = {1},
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 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 %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
Cité par Sources :