Abstract
We study the spectrum of a weighted composition operator T induced by a weight and a holomorphic self-map φ on the unit disc, which is not an elliptic automorphism. If φ has a unique fixed point in , we show that is a bounded discrete set such that is a set of eigenvalues with multiplicity one. If φ has a Denjoy–Wolff point α on the unit circle, we first prove that the point spectrum is whenever is constant. Moreover, the multiplicity of each eigenvalue is infinite. Then we describe classes of m for which the point spectrum of T is either empty or equal to .
Citation
Wolfgang Arendt. Eddy Bernard. Benjamin Célariès. Isabelle Chalendar. "Denjoy–Wolff theory and spectral properties of weighted composition operators on ." Illinois J. Math. 66 (4) 463 - 489, December 2022. https://doi.org/10.1215/00192082-10235589
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