The asymptotic behavior of the spectral function of a one-dimensional second-order differential operator is discussed. We give a necessary and sufficient condition in order that the spectral function varies regularly with index 1. The condition is closely related to the class $\Gamma$ which appears in the de Haan theory.
"Spectral function of Krein’s and Kotani’s string in the class $\Gamma$." Proc. Japan Acad. Ser. A Math. Sci. 88 (10) 173 - 177, December 2012. https://doi.org/10.3792/pjaa.88.173