162748 20251017144621.0 doi 10.1016/j.jfa.2025.111186 sideral 145302 ART-2025-145302 eng Oliva-Maza, Jesús Universidad de Zaragoza (orcid)0000-0001-8546-5883 Spectrum of invertible weighted composition operators on the unit disk 2025 Access copy available to the general public Unrestricted The spectrum of invertible weighted composition operators acting on classical Banach spaces of holomorphic functions in the unit disk has been studied intensively over the years. Complete descriptions of that spectrum have been given in the elliptic or parabolic cases, that is, for φ either elliptic or parabolic, but only partial results have been obtained in the remaining case, that is, for hyperbolic φ. In this paper, we give the spectrum and the essential spectrum of for hyperbolic φ. Our results answer in the positive several conjectures posed by different authors. In order to deal with the above questions, we present new techniques which involve the embedding of the weight u into a cocycle associated to an hyperbolic flow . We also provide information about the range spaces and null spaces of for λ lying in the interior of . info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00 info:eu-repo/semantics/openAccess by-nc https://creativecommons.org/licenses/by-nc/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 290, 1 (2025), 111186 [43 pp.] J. funct. anal. JOURNAL OF FUNCTIONAL ANALYSIS 0022-1236 1714332 http://zaguan.unizar.es/record/162748/files/texto_completo.pdf Versión publicada 1304513 http://zaguan.unizar.es/record/162748/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:162748 articulos driver 2025-10-17-14:22:01 ARTICLE