The spectral form of Koopman representations of the group of measurable functions with values in the circle

2021/07/30 by Justin Tatch Moore, Moore, Justin Tatch, Sławomir Solecki +1
Mathematics · Medicine · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Model Reduction and Neural Networks #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2107.14760

openalex publication_date 2021/07/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/01

Abstract

We compute the spectral form of the Koopman representation induced by a natural boolean action of L⁰(λ, \mathbb T) identified earlier by the authors. Our computation establishes the sharpness of the constraints on spectral forms of Koopman representations of L⁰(λ, \mathbb T) previously found by the second author.

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