Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive-definiteness and integral representations for special functions   We characterize a holomorphic positive definite function $f$ defined on a
horizontal strip of the complex plane as the Fourier-Laplace transform of a
unique exponentially finite measure on $\mathbb{R}$. The classical theorems of
Bochner on positive definite functions and of Widder on exponentially convex
functions become special cases of this characterization: they are respectively
the real and pure imaginary sections of the complex integral representation. We
apply this representation to special cases, including the $\Gamma$, $\zeta$ and
Bessel functions, and construct explicitly the corresponding measures, thus
providing new insight into the nature of complex positive and co-positive
definite functions: in the case of the zeta function this process leads to a
new proof of an integral representation on the critical strip.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat