Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier decay of self-similar measures and self-similar sets of
  uniqueness   In this paper, we investigate the Fourier transform of self-similar measures
on R. We provide quantitative decay rates of Fourier transform of some
self-similar measures. Our method is based on random walks on lattices and
Diophantine approximation in number fields. We also completely identify all
self-similar sets which are sets of uniqueness. This generalizes a classical
result of Salem and Zygmund.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs