Some spherical uniqueness theorems for multiple trigonometric series
| dc.creator | Ash, J. Marshall | |
| dc.creator | Wang, Gang | |
| dc.date | 2000-08-03 | |
| dc.date.accessioned | 2026-07-07T04:36:39Z | |
| dc.date.available | 2026-07-07T04:36:39Z | |
| dc.description | We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the coefficients of the multiple trigonometric series satisfy a mild growth condition. As a consequence, we show that if a multiple trigonometric series is spherically convergent everywhere to an everywhere finite integrable function $f(x)$, then the series is the Fourier series of $f(x)$. We also show that a singleton is a set of uniqueness. These results are generalizations of a recent theorem of J. Bourgain and some results of V. Shapiro. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0008031 | |
| dc.identifier | http://arxiv.org/abs/math/0008031 | |
| dc.identifier | Ann. of Math. (2) 151 (2000), no. 1, 1--33 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59674 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B05;42B99 | |
| dc.title | Some spherical uniqueness theorems for multiple trigonometric series | |
| dc.type | text |