Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^2$ Interpolation with Range Restriction   Given $ -\infty< \lambda < \Lambda < \infty $, $ E \subset \mathbb{R}^n $
finite, and $ f : E \to [\lambda,\Lambda] $, how can we extend $ f $ to a $
C^m(\mathbb{R}^n) $ function $ F $ such that $ \lambda\leq F \leq \Lambda $ and
$ ||F||_{C^m(\mathbb{R}^n)} $ is within a constant multiple of the least
possible, with the constant depending only on $ m $ and $ n $? In this paper,
we provide the solution to the problem for the case $ m = 2 $. Specifically, we
construct a (parameter-dependent, nonlinear) $ C^2(\mathbb{R}^n) $ extension
operator that preserves the range $[\lambda,\Lambda]$, and we provide an
efficient algorithm to compute such an extension using $ O(N\log N) $
operations, where $ N = #(E) $.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex