Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight framelets and fast framelet filter bank transforms on manifolds   Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$
provide a tool of multiresolution analysis for data from geosciences,
astrophysics, medical sciences, etc. This work investigates the construction,
characterizations, and applications of tight framelets on such a manifold
$\mathcal{M}$. Characterizations of the tightness of a sequence of framelet
systems for $L_{2}(\mathcal{M})$ in both the continuous and semi-discrete
settings are provided. Tight framelets associated with framelet filter banks on
$\mathcal{M}$ can then be easily designed and fast framelet filter bank
transforms on $\mathcal{M}$ are shown to be realizable with nearly linear
computational complexity. Explicit construction of tight framelets on the
sphere $\mathbb{S}^{2}$ as well as numerical examples are given.

3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat