Asymptotics of determinants of Bessel operators
Functional Analysis
2009-11-07 v1 Mathematical Physics
math.MP
Abstract
In this paper we determine the asymptotics of the determinant of Bessel operators for sufficiently smooth generating functions. These operators are similar to Wiener-Hopf operators with the Fourier transform replaced by the Hankel transform and thus the asymptotics of the determinanst are similar to the well-known Szeg\"o-Akhiezer-Kac formula for truncated Wiener-Hopf determinants. In order to compute the above, we also show that the Bessel operators differ from the Wiener-Hopf by a Hilbert-Schmidt operator.
Keywords
Cite
@article{arxiv.math/0204304,
title = {Asymptotics of determinants of Bessel operators},
author = {Estelle L. Basor and Torsten Ehrhardt},
journal= {arXiv preprint arXiv:math/0204304},
year = {2009}
}