Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Method to solve integral equations of the first kind with an approximate
  input   Techniques are proposed for solving integral equations of the first kind with
an input known not precisely. The requirement that the solution sought for
includes a given number of maxima and minima is imposed. It is shown that when
the deviation of the approximate input from the true one is sufficiently small
and some additional conditions are fulfilled the method leads to an approximate
solution that is necessarily close to the true solution. No regularization is
required in the present approach. Requirements on features of the solution at
integration limits are also imposed. The problem is treated with the help of an
ansatz proposed for the derivative of the solution. The ansatz is the most
general one compatible with the above mentioned requirements. The techniques
are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes
and Laplace integral transforms are performed, and very satisfactory results
are obtained. The method is useful, in particular, for the calculation of
quantum-mechanical reaction amplitudes and inclusive spectra of
perturbation-induced reactions in the framework of the integral transform
approach.

35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph