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arxiv: math/0204304 · v1 · submitted 2002-04-24 · 🧮 math.FA · math-ph· math.MP

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Asymptotics of determinants of Bessel operators

Estelle L. Basor , Torsten Ehrhardt
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classification 🧮 math.FA math-phmath.MP
keywords operatorsasymptoticsbesselwiener-hopfdeterminantssimilartransformabove
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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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  1. Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel

    hep-th 2026-02 unverdicted novelty 6.0

    Reorganizing the transseries of matrix Bessel kernel determinants at strong coupling yields a simple structure where non-perturbative corrections are directly determined by the perturbative series for N=4 SYM observables.