Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral properties and self-adjoint extensions of the third power of
  the radial Laplace operator   We consider self-adjoint extensions of differential operators of the type $
(-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2
with two kinds of boundary conditions: first that nullify the value of a
function and its first derivative and second that nullify the 4th (l=1) or the
3rd (l=2) derivative. We calculate the expressions for the correponding
resolvents and derive spectral decompositions. These types of boundary
conditions are interesting from the physical point of view, especially the
second ones, which give an example of emergence of long-range action in
exchange for a singularity at the origin.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph