Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series
| dc.creator | Bhatt, S. J. | |
| dc.creator | Dedania, H. V. | |
| dc.date | 2003-10-18 | |
| dc.date.accessioned | 2026-07-07T05:02:04Z | |
| dc.date.available | 2026-07-07T05:02:04Z | |
| dc.description | Let $f$ be a continuous function on the unit circle $Γ$, whose Fourier series is $ω$-absolutely convergent for some weight $ω$ on the set of integers $\mathcal{Z}$. If $f$ is nowhere vanishing on $Γ$, then there exists a weight $ν$ on $\mathcal{Z}$ such that $1/f$ had $ν$-absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if $ϕ$ is holomorphic on a neighbourhood of the range of $f$, then there exists a weight $χ$ on $\mathcal{Z}$ such that \hbox{$ϕ\circ f$} has $χ$-absolutely convergent Fourier series. This is a weighted analogue of Lévy's generalization of Wiener's theorem. In the theorems, $ν$ and $χ$ are non-constant if and only if $ω$ is non-constant. In general, the results fail if $ν$ or $χ$ is required to be the same weight $ω$. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310291 | |
| dc.identifier | http://arxiv.org/abs/math/0310291 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 2, May 2003, pp. 179-182 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68909 | |
| dc.subject | Complex Variables | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series | |
| dc.type | text |