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- W2951567111 abstract "Let $J_k^alpha$ 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 $A_k=bigoplus_{j=1}^n lambda_j J_k^alpha$ 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 $mu_{A_k}$ 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(Aoplus B)=Hyplat Aoplus Hyplat BRightarrow Lat(Aoplus B)=Lat Aoplus Lat B to be valid." @default.
- W2951567111 created "2019-06-27" @default.
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- W2951567111 date "2009-03-24" @default.
- W2951567111 modified "2023-09-27" @default.
- W2951567111 title "On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions" @default.
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