- Tytuł:
- Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on $^n$ and on compact Lie groups)
- Autorzy:
- Travaglini, Giancarlo
- Powiązania:
- https://bibliotekanauki.pl/articles/967329.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
polyhedral Dirichlet kernels
multiple Fourier series
Fourier series on compact Lie groups
Lebesgue constants - Opis:
- 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.
- Źródło:
-
Colloquium Mathematicum; 1993, 65, 1; 103-116
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł