Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Averaged mixed Julia-Fatou type theory with applications to spectral
  foliation   Classically, theorems of Fatou and Julia describe the boundary regularity of
functions in one complex variable. The former says that a complex analytic
function on the disk has non-tangential boundary values almost everywhere, and
the latter describes when a function takes an extreme value at a boundary point
and is differentiable there non-tangentially. We describe a class of
intermediate theorems in terms of averaged Julia-Fatou quotients. Boundary
regularity is related to integrability of certain quantities against a special
measure, the so-called Nevanlinna measure. Applications are given to spectral
theory.

37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph