Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry problems in harmonic analysis   Symmetry problems in harmonic analysis are formulated and solved. One of
these problems is equivalent to the refined Schiffer's conjecture which was
recently proved by the author. Let $k=const>0$ be fixed, $S^2$ be the unit
sphere in $\mathbb{R}^3$, $D$ be a connected bounded domain with $C^2-$smooth
boundary $S$, $j_0(r)$ be the spherical Bessel function. The harmonic analysis
symmetry problems are stated in the following theorems:
  {\bf Theorem A.} {\em Assume that $\int_S e^{ik\beta \cdot s}ds=0$ for all
$\beta\in S^2$. Then $S$ is a sphere of radius $a$, where $j_0(ka)=0$. }
  {\bf Theorem B.} {\em Assume that $\int_D e^{ik\beta \cdot x}dx=0$ for all
$\beta\in S^2$. Then $D$ is a ball.

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The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg