Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A regularity class for the roots of non-negative functions   We investigate the regularity of the positive roots of a non-negative
function of one-variable. A modified H\"older space $\mathcal{F}^\beta$ is
introduced such that if $f\in \mathcal{F}^\beta$ then $f^\alpha \in C^{\alpha
\beta}$. This provides sufficient conditions to overcome the usual limitation
in the square root case ($\alpha = 1/2$) for H\"older functions that $f^{1/2}$
need be no more than $C^1$ in general. We also derive bounds on the wavelet
coefficients of $f^\alpha$, which provide a finer understanding of its local
regularity.

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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn