Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Around multivariate Schmidt-Spitzer theorem   Given an arbitrary complex-valued infinite matrix A and a positive integer n
we introduce a naturally associated polynomial basis B_A of C[x0...xn]. We
discuss some properties of the locus of common zeros of all polynomials in B_A
having a given degree m; the latter locus can be interpreted as the spectrum of
the m*(m+n)-submatrix of A formed by its m first rows and m+n first columns. We
initiate the study of the asymptotics of these spectra when m goes to infinity
in the case when A is a banded Toeplitz matrix. In particular, we present and
partially prove a conjectural multivariate analog of the well-known
Schmidt-Spitzer theorem which describes the spectral asymptotics for the
sequence of principal minors of an arbitrary banded Toeplitz matrix. Finally,
we discuss relations between polynomial bases B_A and multivariate orthogonal
polynomials.

36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex