Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators
  in Sobolev Spaces of Vector Functions   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(A\oplus B)=\Hyplat A\oplus \Hyplat B\Rightarrow \Lat(A\oplus B)=\Lat
A\oplus \Lat B to be valid.

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph