127559 20241125101142.0 doi 10.1007/s43034-023-00290-0 sideral 134550 ART-2023-134550 eng Miana, Pedro J. Universidad de Zaragoza (orcid)0000-0001-9430-343X Catalan generating functions for bounded operators 2023 Access copy available to the general public Unrestricted In this paper, we study the solution of the quadratic equation TY2−Y+I=0 where T is a linear and bounded operator on a Banach space X. We describe the spectrum set and the resolvent operator of Y in terms of the ones of T. In the case that 4T is a power-bounded operator, we show that a solution (named Catalan generating function) of the above equation is given by the Taylor series C(T):=∑n=0∞CnTn, where the sequence (Cn)nis the well-known Catalan numbers sequence. We express C(T) by means of an integral representation which involves the resolvent operator (λT)−1. Some particular examples to illustrate our results are given, in particular an iterative method defined for square matrices T which involves Catalan numbers info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.2 2023 MATHEMATICS 80 / 490 = 0.163 2023 Q1 T1 MATHEMATICS, APPLIED 140 / 332 = 0.422 2023 Q2 T2 0.523 2023 Algebra and Number Theory 2023 Q2 Control and Optimization 2023 Q2 Analysis 2023 Q2 2.0 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Romero, Natalia 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 14, 69 (2023), 21 Ann. funct. analysis Annals of functional analysis 2639-7390 733190 http://zaguan.unizar.es/record/127559/files/texto_completo.pdf Versión publicada 963809 http://zaguan.unizar.es/record/127559/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:127559 articulos driver 2024-11-22-12:03:00 ARTICLE