%0 Journal Article
%A Monsalve López, Miguel
%A Seco, Daniel
%T Towards spectral descriptions of cyclic functions
%D 2025
%U https://hdl.handle.net/20.500.14352/128676
%X 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 $H^2$ of the function $z \mapsto a − z$ 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.
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