Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the Cauchy functional equation and variations of it   This paper examines various aspects related to the Cauchy functional equation
$f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional
equations. In particular, it considers its solvability and its stability
relative to subsets of multi-dimensional Euclidean spaces and tori. Several new
types of regularity conditions are introduced, such as a one in which a complex
exponent of the unknown function is locally measurable. An initial value
approach to analyzing this equation is considered too and it yields a few
by-products, such as the existence of a non-constant real function having an
uncountable set of periods which are linearly independent over the rationals.
The analysis is extended to related equations such as the Jensen equation, the
multiplicative Cauchy equation, and the Pexider equation. The paper also
includes a rather comprehensive survey of the history of the Cauchy equation.

14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat