# Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on ${}^{n}$ and on compact Lie groups)

Colloquium Mathematicae (1993)

- Volume: 65, Issue: 1, page 103-116
- ISSN: 0010-1354

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topTravaglini, Giancarlo. "Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $^n$ and on compact Lie groups)." Colloquium Mathematicae 65.1 (1993): 103-116. <http://eudml.org/doc/210195>.

@article{Travaglini1993,

abstract = {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.},

author = {Travaglini, Giancarlo},

journal = {Colloquium Mathematicae},

keywords = {Fourier series on compact Lie groups; Lebesgue constants; polyhedral Dirichlet kernels; multiple Fourier series; approximation; summability; asymptotic formula},

language = {eng},

number = {1},

pages = {103-116},

title = {Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $^n$ and on compact Lie groups)},

url = {http://eudml.org/doc/210195},

volume = {65},

year = {1993},

}

TY - JOUR

AU - Travaglini, Giancarlo

TI - Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $^n$ and on compact Lie groups)

JO - Colloquium Mathematicae

PY - 1993

VL - 65

IS - 1

SP - 103

EP - 116

AB - 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.

LA - eng

KW - Fourier series on compact Lie groups; Lebesgue constants; polyhedral Dirichlet kernels; multiple Fourier series; approximation; summability; asymptotic formula

UR - http://eudml.org/doc/210195

ER -

## References

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