Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fractal uncertainty principle for Bergman spaces and analytic wavelets   Motivated by results of Dyatlov on Fourier uncertainty principles for Cantor
sets and of Knutsen, for joint time-frequency representations (STFT with
Gaussian, equivalent to Fock spaces), we suggest a general setting relating
localization and uncertainty and prove, within this context, an uncertainty
principle for Cantor sets in Bergman spaces of the unit disc, defined as unions
of annuli equidistributed in the hyperbolic measure. The result can be written
in terms of analytic Cauchy wavelets. As in the case of the STFT considered by
Knutsen, our result consists of a double side bound for the norm of a
localization operator involving the fractal dimension log2/log3 in the
exponent. As in the STFT case and in Dyatlov's fractal uncertainty principle,
the norm of the dilated iterates of the Cantor set in the disc tends to
infinite, while the corresponding norm of the localization operator tends to
zero.

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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci