Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wavelet decomposition and bandwidth of functions defined on vector
  spaces over finite fields   In this paper we study how zeros of the Fourier transform of a function $f:
\mathbb{Z}_p^d \to \mathbb{C}$ are related to the structure of the function
itself. In particular, we introduce a notion of bandwidth of such functions and
discuss its connection with the decomposition of this function into wavelets.
Connections of these concepts with the tomography principle and the
Nyquist-Shannon sampling theorem are explored.
  We examine a variety of cases such as when the Fourier transform of the
characteristic function of a set $E$ vanishes on specific sets of points,
affine subspaces, and algebraic curves. In each of these cases, we prove
properties such as equidistribution of $E$ across various surfaces and bounds
on the size of $E$.
  We also establish a finite field Heisenberg uncertainty principle for sets
that relates their bandwidth dimension and spatial dimension.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph