Spectral decomposition and Gelfand's theorem
| dc.creator | Driouich, A. | |
| dc.creator | El-Mennaoui, O. | |
| dc.creator | Jazar, M. | |
| dc.date | 2005-05-20 | |
| dc.date | 2007-10-31 | |
| dc.date.accessioned | 2026-07-07T08:39:33Z | |
| dc.date.available | 2026-07-07T08:39:33Z | |
| dc.description | In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if $A$ generates a polynomially bounded $n$-times integrated group whose spectrum set $σ(A)=\{iλ_k; k\in\mathbb{Z}^* \}$ is discrete and satisfies $\sum \frac{1}{|λ_k|^\ellδ_k^n}<\infty$ ($n$ and $\ell$ nonnegative integers), then there exists projectors $(P_k)_{k\in\mathbb{Z}^*}$ such that $\sum P_kx=x$ ($ x\in D(A^{n+\ell})$), where $δ_k=\min(\frac{| λ_{k+1}-λ_k|}2, \frac{|λ_{k-1}-λ_k|}2)$. | |
| dc.description | 15 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0505428 | |
| dc.identifier | http://arxiv.org/abs/math/0505428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141111 | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A60, 47A10, 47D03, 47D06, 47D62 (Primary) 47A10 (Secondary) | |
| dc.title | Spectral decomposition and Gelfand's theorem | |
| dc.type | text |