Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recasting the Proof of Parseval's Identity   We generalize aspects of Fourier Analysis from intervals on $\mathbb{R}$ to
bounded and measurable subsets of $\mathbb{R}^n$. In doing so, we obtain a few
interesting results. The first is a new proof of the famous Integral
Cauchy-Schwarz Inequality. The second is a restatement of Parseval's Identity
that doubles as a representation of integrating bounded and measurable
functions over bounded and measurable subsets of $\mathbb{R}^n$. Finally, we
apply these first two results to develop some sufficient criteria for
additional integral inequalities that are elementary in nature.

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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin