Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-extension estimates for symmetric functions and applications to
  nonlinear Helmholtz equations   We establish weighted $L^p$-Fourier-extension estimates for $O(N-k) \times
O(k)$-invariant functions defined on the unit sphere $\mathbb{S}^{N-1}$,
allowing for exponents $p$ below the Stein-Tomas critical exponent
$\frac{2(N+1)}{N-1}$. Moreover, in the more general setting of an arbitrary
closed subgroup $G \subset O(N)$ and $G$-invariant functions, we study the
implications of weighted Fourier-extension estimates with regard to boundedness
and nonvanishing properties of the corresponding weighted Helmholtz resolvent
operator. Finally, we use these properties to derive new existence results for
$G$-invariant solutions to the nonlinear Helmholtz equation
  $$ - \Delta u - u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N}), $$
where $Q$ is a nonnegative bounded and $G$-invariant weight function.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin