The spectral analysis of the difference quotient operator on model spaces

2024/10/24 by Carlo Bellavita, Eugenio Dellepiane, Bellavita, Carlo +3 · 1 citation
Mathematics · #30H10 #47A10 #Complex Variables (math.CV) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2410.18623

openalex publication_date 2024/10/24 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

We conduct a spectral analysis of the difference quotient operator Q^u_ζ, associated with a boundary point ζ∈ ∂ \mathbbD, 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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