Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant subspaces of elliptic systems I: pseudodifferential
  projections   Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on
$m$-columns of half-densities on a closed manifold $M$, whose principal symbol
is assumed to have simple eigenvalues. We show existence and uniqueness of $m$
orthonormal pseudodifferential projections commuting with the operator $A$ and
provide an algorithm for the computation of their full symbols, as well as
explicit closed formulae for their subprincipal symbols. Pseudodifferential
projections yield a decomposition of $L^2(M)$ into invariant subspaces under
the action of $A$ modulo $C^\infty(M)$. Furthermore, they allow us to decompose
$A$ into $m$ distinct sign definite pseudodifferential operators. Finally, we
represent the modulus and the Heaviside function of the operator $A$ in terms
of pseudodifferential projections and discuss physically meaningful examples.

6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph