Abstract
In this paper an asymptotic formula is given for the Lebesgue constants generated by the anisotropically dilated d-dimensional simplex. Contrary to many preceding results established only in dimension two, the obtained ones are proved in any dimension. Also, the “rational” and “irrational” parts are both united and separated in one formula.
| Original language | English |
|---|---|
| Pages (from-to) | 2911-2926 |
| Number of pages | 16 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 149 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2021 |
Bibliographical note
Publisher Copyright:2021 American Mathematical Society
Funding
Received by the editors April 23, 2020, and, in revised form, October 22, 2020. 2020 Mathematics Subject Classification. Primary 42B05, 42B08, 42A05. Key words and phrases. Lebesgue constants, asymptotic formula, anisotropy, Dirichlet kernel, d-dimensional simplex. The first author was supported by DFG project KO 5804/1-1.
| Funders | Funder number |
|---|---|
| Deutsche Forschungsgemeinschaft | KO 5804/1-1 |
Keywords
- Anisotropy
- Asymptotic formula
- D-dimensional simplex
- Dirichlet kernel
- Lebesgue constants