Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\Psi$ec: A Local Spectral Exterior Calculus   We introduce $\Psi \mathrm{ec}$, a discretization of Cartan's exterior
calculus of differential forms using wavelets. Our construction consists of
differential $r$-form wavelets with flexible directional localization that
provide tight frames for the spaces $\Omega^r(\mathbb{R}^n)$ of forms in
$\mathbb{R}^2$ and $\mathbb{R}^3$. By construction, the wavelets satisfy the de
Rahm co-chain complex, the Hodge decomposition, and that the $k$-dimensional
integral of an $r$-form is an $(r-k)$-form. They also verify Stokes' theorem
for differential forms, with the most efficient finite dimensional
approximation attained using directionally localized, curvelet- or
ridgelet-like forms. The construction of $\Psi \mathrm{ec}$ builds on the
geometric simplicity of the exterior calculus in the Fourier domain. We
establish this structure by extending existing results on the Fourier transform
of differential forms to a frequency description of the exterior calculus,
including, for example, a Plancherel theorem for forms and a description of the
symbols of all important operators.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn