Asymptotics of determinants of Bessel operators

Details Asymptotics of determinants of Bessel operators Asymptotics of determinants of Bessel operators

2002-04-24

arxiv.org/abs/math/0204304v1

Mathematics

Functional Analysis

Scientific paper

10.1007/s00220-002-0769-1

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.

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