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arXiv · 2410.18623

The spectral analysis of the difference quotient operator on model spaces

Carlo Bellavita·Eugenio Alberto Dellepiane·Javad Mashreghi
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Abstract

We conduct a spectral analysis of the difference quotient operator $Q^u_\zeta$, associated with a boundary point $\zeta \in \partial \mathbb{D}$, on the model space $K_u$. We describe the operator's spectrum and provide both upper and lower estimates for its norm, and furthermore discussing the sharpness of these bounds. Notably, the upper estimate offers a new characterization of the one-component property for inner function.

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Carlo Bellavita, Eugenio Alberto Dellepiane, Javad Mashreghi. 2024-10-24. The spectral analysis of the difference quotient operator on model spaces. https://arxiv.org/abs/2410.18623

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