Lacunarity and cyclic vectors for the Backward Shift
| dc.creator | Choukrallah, Reda | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T08:50:39Z | |
| dc.date.available | 2026-07-07T08:50:39Z | |
| dc.description | This article gives a description of invariant subspaces for the backward shift generated by vector valued lacunary series and by a class of lacunary power series in $H^2(\mathbb{D}, X)$, (where $X$ is an Hilbert space). In particular, we show that these series $f$ in $H^2(\mathbb{D}, X)$ are cyclic vectors if and only if the queue of Taylor coefficients $\{\hat{f}(k)$, $k>N\}$ generates the whole space $X$. Analogues of this result are obtained for some functions whose spectrum is a finite union of lacunary sequences and in the polydisc. In the scalar case $H^2$, we give a criterion on the Fourier spectrum of the function to have cyclicity for any power of the backward shift. | |
| dc.identifier | https://arxiv.org/abs/0712.3486 | |
| dc.identifier | http://arxiv.org/abs/0712.3486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144672 | |
| dc.subject | Spectral Theory | |
| dc.title | Lacunarity and cyclic vectors for the Backward Shift | |
| dc.type | text |