Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-differential operators, heat calculus and index theory of
  groupoids satisfying the Lauter-Nistor condition   In this thesis, we study singular pseudo-differential operators defined by
groupoids satisfying the Lauter-Nistor condition, by a method parallel to that
of manifolds with boundary and edge differential operators. The example of the
Bruhat sphere is studied in detail. In particular, we construct an extension to
the calculus of uniformly supported pseudo-differential operators that is
analogous to the calculus with bounds defined on manifolds with boundary. We
derive a Fredholmness criterion for operators on the Bruhat sphere, and prove
that their parametrices up to compact operators lie inside the extended
calculus; we construct the heat kernel of perturbed Laplacian operators; and
prove an Atiyah-Singer type renormalized index formula for perturbed Dirac
operators on the Bruhat sphere using the heat kernel method.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio