Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convolutions on the Sphere: Commutation with Differential Operators   We generalize the definition of convolution of vectors and tensors on the
2-sphere, and prove that it commutes with differential operators. Moreover,
vectors and tensors that are normal/tangent to the spherical surface remain so
after the convolution. These properties make the new filtering operation
particularly useful to analyzing and modeling nonlinear dynamics in spherical
systems, such as in geophysics, astrophysics, and in inertial confinement
fusion applications. An essential tool we use is the theory of scalar, vector,
and tensor spherical harmonics. We then show that our generalized filtering
operation is equivalent to the (traditional) convolution of scalar fields of
the Helmholtz decomposition of vectors and tensors.

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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg