Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the vanishing of Green's function, desingularization and Carleman's
  method   The subject of the present paper is the phenomenon of vanishing of the Green
function of the operator $-\Delta + V$ on $\mathbb R^3$ at the points where a
potential $V$ has positive critical singularities. More precisely, imposing
minimal assumptions on $V$ (i.e. the form-boundedness), we obtain an upper
bound on the order of vanishing of the Green function. As a by-product of our
proof, we improve the existing results on the strong unique continuation for
eigenfunctions of $-\Delta + V$ in dimension $d=3$.

35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org