Symmetries and reflections from composition operators in the disk

2023/07/03 by Andruchow, Esteban, Corach, Gustavo, Recht, Lázaro
#47A05 #47B15 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.01287

Abstract

We study the composition operators C_a acting on the Hardy space H² of the unit disk, given by C_af=f∘φ_a, where φ_a(z)=\fraca-z1-az, for |a|<1. These operators are reflections: C_a²=1. We study their eigenspaces N(C_a± 1), their relative position (i.e., the intersections between these spaces and their orthogonal complementes for a≠ b in the unit disk) and the symmetries induced by C_a and these eigenspaces.

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