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arXiv · 2411.15578

Functions of continuous Ces\'aro operators

Adolf Mirotin
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Abstract

We describe holomorphic functions and fractional powers of Ces\'{a}ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces\'{a}ro operators are introduced as well and their spectral properties are studied. Several examples are considered.

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Adolf Mirotin. 2024-11-23. Functions of continuous Ces\'aro operators. https://arxiv.org/abs/2411.15578

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