000162748 001__ 162748 000162748 005__ 20251017144621.0 000162748 0247_ $$2doi$$a10.1016/j.jfa.2025.111186 000162748 0248_ $$2sideral$$a145302 000162748 037__ $$aART-2025-145302 000162748 041__ $$aeng 000162748 100__ $$0(orcid)0000-0001-8546-5883$$aOliva-Maza, Jesús$$uUniversidad de Zaragoza 000162748 245__ $$aSpectrum of invertible weighted composition operators on the unit disk 000162748 260__ $$c2025 000162748 5060_ $$aAccess copy available to the general public$$fUnrestricted 000162748 5203_ $$aThe 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 . 000162748 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00 000162748 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttps://creativecommons.org/licenses/by-nc/4.0/deed.es 000162748 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000162748 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000162748 773__ $$g290, 1 (2025), 111186 [43 pp.]$$pJ. funct. anal.$$tJOURNAL OF FUNCTIONAL ANALYSIS$$x0022-1236 000162748 8564_ $$s1714332$$uhttps://zaguan.unizar.es/record/162748/files/texto_completo.pdf$$yVersión publicada 000162748 8564_ $$s1304513$$uhttps://zaguan.unizar.es/record/162748/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000162748 909CO $$ooai:zaguan.unizar.es:162748$$particulos$$pdriver 000162748 951__ $$a2025-10-17-14:22:01 000162748 980__ $$aARTICLE