Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal polynomial projection error measured in Sobolev norms in the
  unit disk   We study approximation properties of weighted $L^2$-orthogonal projectors
onto the space of polynomials of degree less than or equal to $N$ on the unit
disk where the weight is of the generalized Gegenbauer form $x \mapsto
(1-|x|^2)^\alpha$. The approximation properties are measured in Sobolev-type
norms involving canonical weak derivatives, all measured in the same weighted
$L^2$ norm. Our basic tool consists in the analysis of orthogonal expansions
with respect to Zernike polynomials. The sharpness of the main result is proved
in some cases and otherwise strongly hinted at by reported numerical tests.
  A number of auxiliary results of independent interest are obtained including
some properties of the uniformly and non-uniformly weighted Sobolev spaces
involved, a Markov-type inequality, connection coefficients between Zernike
polynomials and relations between the Fourier-Zernike expansions of a function
and its derivatives.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph