On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions
| dc.creator | Domanov, I. Yu. | |
| dc.creator | Malamud, M. M. | |
| dc.date | 2009-03-24 | |
| dc.date.accessioned | 2026-07-07T12:56:05Z | |
| dc.date.available | 2026-07-07T12:56:05Z | |
| dc.description | Let $J_k^α$ be a real power of the integration operator $J_k$ defined on Sobolev space $W_p^k[0,1]$. We investigate the spectral properties of the operator $A_k=\bigoplus_{j=1}^n λ_j J_k^α$ defined on $\bigoplus_{j=1}^n W_p^k[0,1]$. Namely, we describe the commutant $\{A_k\}'$, the double commutant $\{A_k\}''$ and the algebra $\Alg A_k$. Moreover, we describe the lattices $\Lat A_k$ and $\Hyplat A_k$ of invariant and hyperinvariant subspaces of $A_k$, respectively. We also calculate the spectral multiplicity $μ_{A_k}$ of $A_k$ and describe the set $\Cyc A_k$ of its cyclic subspaces. In passing, we present a simple counterexample for the implication \Hyplat(A\oplus B)=\Hyplat A\oplus \Hyplat B\Rightarrow \Lat(A\oplus B)=\Lat A\oplus \Lat B to be valid. | |
| dc.description | published in Integr. equ. oper. theory 63 (2009), 181-215 | |
| dc.identifier | https://arxiv.org/abs/0903.4069 | |
| dc.identifier | http://arxiv.org/abs/0903.4069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224467 | |
| dc.subject | Spectral Theory | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A15, 47A16, 47L80 (Primary) 47L10 (Secondary) | |
| dc.title | On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions | |
| dc.type | text |