Towards spectral descriptions of cyclic functions Towards spectral descriptions of cyclic functions

We build on a characterization of inner functions f due to Le, in terms of the spectral properties of the operator V = M f ∗ M f and study to what extent the cyclicity on weighted Hardy spaces H ω 2 of the function z ↦ a - z can be similarly inferred from the spectral properties of the corresponding...

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Bibliographic Details
Published inAnnals of functional analysis Vol. 16; no. 3
Main Authors Monsalve-López, Miguel, Seco, Daniel
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2025
Subjects
Functional Analysis
Mathematics
Mathematics and Statistics
Original Paper
Inner functions
47A16
30J05
Multiplication operators
Point spectrum
47B32
Reproducing kernel Hilbert spaces
47A10
Cyclic functions
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ISSN2639-7390
2008-8752
DOI10.1007/s43034-025-00446-0

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Summary:We build on a characterization of inner functions f due to Le, in terms of the spectral properties of the operator V = M f ∗ M f and study to what extent the cyclicity on weighted Hardy spaces H ω 2 of the function z ↦ a - z can be similarly inferred from the spectral properties of the corresponding operator V . We describe several properties of the spectra that hold in a large class of spaces and then, we focus on the particular case of Bergman-type spaces, for which we describe completely the spectrum of such operators and find all eigenfunctions.
ISSN:2639-7390
2008-8752
DOI:10.1007/s43034-025-00446-0