Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operators that coerce the surjectivity of convolution   Considered are operators that leave the set of non-invertible (in the sense
of Ehrenpreis) distributions stable. They simultaneously generalise the
operation of convolution by a distribution with compact support and the
operation of multiplication by a real analytic function; they are here called
pseudo-convolutions since they also generalise pseudo-differential operators.
(It is shown that the elliptic real analytic pseudo-differential operators
leave both the non-invertible and the invertible distributions invariant.) But
when the condition of real-analyticity is relaxed, such operators may map a
non-invertible distribution to one invertible -- given that the invertibility
in both cases concerns the same function space. By varying the space, however,
one can measure the 'loss of non-invertibily' that a non-analytic perturbation
may introduce. This phenomenon is here studied using the Beurling classes of
functions and measuring the regularity of operator symbols in the
Denjoy-Carleman sense; the Gevrey case turns out particularly simple.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys