Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sturm-Liouville hypergroups without the compactness axiom   We establish a positive product formula for the solutions of the
Sturm-Liouville equation $\ell(u) = \lambda u$, where $\ell$ belongs to a
general class which includes singular and degenerate Sturm-Liouville operators.
Our technique relies on a positivity theorem for possibly degenerate hyperbolic
Cauchy problems and on a regularization method which makes use of the
properties of the diffusion semigroup generated by the Sturm-Liouville
operator.
  We show that the product formula gives rise to a convolution algebra
structure on the space of finite measures, and we discuss whether this
structure satisfies the basic axioms of the theory of hypergroups. We introduce
the notion of a degenerate hypergroup of full support and improve the known
existence theorems for Sturm-Liouville hypergroups. Convolution-type integral
equations on weighted Lebesgue spaces are also introduced, and a solvability
condition is established.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin