Monsalve López, MiguelSeco, Daniel2025-12-102025-12-102025Monsalve-López, M., Seco, D. Towards spectral descriptions of cyclic functions. Ann. Funct. Anal. 16, 52 (2025)10.1007/s43034-025-00446-0https://hdl.handle.net/20.500.14352/1286762025 Acuerdos transformativos CRUEWe 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.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://doi.org/10.1007/s43034-025-00446-0open accessInner functionsCyclic functionsMultiplication operatorsReproducing kernel Hilbert spacesPoint spectrumAnálisis funcional y teoría de operadores1202.14 Espacio de Hilbert1202.09 Funciones de Una Variable Compleja