The truncated Fourier operator. I
| dc.creator | Katsnelson, Victor | |
| dc.creator | Machluf, Ronny | |
| dc.date | 2009-01-16 | |
| dc.date.accessioned | 2026-07-07T12:31:07Z | |
| dc.date.available | 2026-07-07T12:31:07Z | |
| dc.description | Let (\mathscr{F}) be the one dimensional Fourier-Plancherel operator and (E) be a subset of the real axis. The truncated Fourier operator is the operator (\mathscr{F}_E) of the form (\mathscr{F}_E=P_E\mathscr{F}P_E), where ((P_Ex)(t)=χ_E(t)x(t)), and (χ_E(t)) is the indicator function of the set (E). In the presented first part of the work, the basic properties of the operator (\mathscr{F}_E) according to the set (E) are discussed. Among these properties there are the following one. The operator (\mathscr{F}_E): 1. has a not-trivial null-space; 2. is strictly contractive; 3. is a normal operator; 4. is a Hilbert-Schmidt operator; 5. is a trace class operator. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0901.2555 | |
| dc.identifier | http://arxiv.org/abs/0901.2555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216346 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A38, 47B35, 47B06, 47A10 | |
| dc.title | The truncated Fourier operator. I | |
| dc.type | text |