Catalan generating functions for bounded operators

Miana, Pedro J. (Universidad de Zaragoza) ; Romero, Natalia

Resumen: 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

Idioma: Inglés

DOI: 10.1007/s43034-023-00290-0

Año: 2023

Publicado en: Annals of functional analysis 14, 69 (2023), 21
ISSN: 2639-7390

Factor impacto JCR: 1.2 (2023)

Categ. JCR: MATHEMATICS rank: 80 / 490 = 0.163 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 140 / 332 = 0.422 (2023) - Q2 - T2

Factor impacto CITESCORE: 2.0 - Analysis (Q2) - Algebra and Number Theory (Q2)

Factor impacto SCIMAGO: 0.523 - Algebra and Number Theory (Q2) - Control and Optimization (Q2) - Analysis (Q2)

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)