Positivity conditions on the annulus via the double-layer potential kernel

07/25/2023

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by   Michael T. Jury, et al.

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We introduce and study a scale of operator classes on the annulus that is motivated by the 𝒞_ρ classes of ρ-contractions of Nagy and Foiaş. In particular, our classes are defined in terms of the contractivity of the double-layer potential integral operator over the annulus. We prove that if, in addition, complete contractivity is assumed, then one obtains a complete characterization involving certain variants of the 𝒞_ρ classes. Recent work of Crouzeix-Greenbaum and Schwenninger-de Vries allows us to also obtain relevant K-spectral estimates, generalizing existing results from the literature on the annulus. Finally, we exhibit a special case where these estimates can be significantly strengthened.