Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the completeness and Riesz basis property of root subspaces of
  boundary value problems for first order systems and applications   The paper is concerned with the completeness property of root functions of
general boundary value problems for $n \times n$ first order systems of
ordinary differential equations on a finite interval. In comparison with the
recent paper [45] we substantially relax the assumptions on boundary conditions
guarantying the completeness of root vectors, allowing them to be non-weakly
regular and even degenerate. Emphasize that in this case the completeness
property substantially depends on the values of a potential matrix at the
endpoints of the interval.
  It is also shown that the system of root vectors of the general $n \times n$
Dirac type system subject to certain boundary conditions forms a Riesz basis
with parentheses. We also show that arbitrary complete dissipative boundary
value problem for Dirac type operator with a summable potential matrix admits
the spectral synthesis in $L^2([0,1]; \mathbb{C}^n)$. Finally, we apply our
results to investigate completeness and the Riesz basis property of the dynamic
generator of spatially non-homogenous damped Timoshenko beam model.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys