Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequalities for Nonuniform Wavelet Frames   Gabardo and Nashed have studied nonuniform wavelets based on the theory of
spectral pairs for which the associated translation set $\Lambda =\left\{
0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but
a spectrum associated with a certain one-dimensional spectral pair and the
associated dilation is an even positive integer related to the given spectral
pair. In this paper, we construct the associated wavelet frames and establish
some sufficient conditions that ensure the nonuniform wavelet system $\left\{
\psi_{j, \lambda}(x)= (2N)^{j/2}\psi\big( (2N)^{j}x-\lambda\big), j\in \mathbb
Z, \lambda\in \Lambda \right\}$ to be a frame for $L^2(\mathbb R)$. The
conditions proposed are stated in terms of the Fourier transforms of the
wavelet system's generating functions.

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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an