Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Multiresolution Analysis and Associated Scaling Functions in
  $L^2(\mathbb R)$   In this paper, we show how to construct an orthonormal basis from Riesz basis
by assuming that the fractional translates of a single function in the core
subspace of the fractional multiresolution analysis form a Riesz basis instead
of an orthonormal basis. In the definition of fractional multiresolution
analysis, we show that the intersection triviality condition follows from the
other conditions. Furthermore, we show that the union density condition also
follows under the assumption that the fractional Fourier transform of the
scaling function is continuous at $0$. At the culmination, we provide the
complete characterization of the scaling functions associated with fractional
multiresolutrion analysis.

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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
27
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: mtrl-th