Abstract
The paper is devoted to first-order trace formulas for the iterates of the Fox–Li and related Wiener–Hopf integral operators. Such formulas provide first insight into the asymptotic behaviour of the eigenvalues and can be used to test whether a specific guess for the eigenvalue distribution is acceptable or not. The main technical problem consists in obtaining the asymptotics of a multivariate oscillatory integral whose stationary points constitute a line.
Mathematics Subject Classification (2000). Primary 47B35; Secondary 45C05, 47B10, 78A60.
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Böttcher, A., Grudsky, S., Huybrechs, D., Iserles, A. (2012). First-order Trace Formulae for the Iterates of the Fox–Li Operator. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_8
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