Treffer: Powers of Catalan generating functions for bounded operators
Title:
Powers of Catalan generating functions for bounded operators
Authors:
Source:
RIUR. Repositorio Institucional de la Universidad de La Rioja
Universidad de La Rioja (UR)
Dialnet CRIS Repositorio institucional de la Universidad de La Rioja
instname
Universidad de La Rioja (UR)
Dialnet CRIS Repositorio institucional de la Universidad de La Rioja
instname
Publication Status:
Preprint
Publisher Information:
Wiley, 2023.
Publication Year:
2023
Subject Terms:
Catalan triangle numbers, Mathematics - Functional Analysis, generating function, Mathematics - Operator Algebras, FOS: Mathematics, powers of bounded operators, 0102 computer and information sciences, 0101 mathematics, quadratic equation, Operator Algebras (math.OA), Catalan triangle numbers, generating function, powers of bounded operators, quadratic equation, 01 natural sciences, Functional Analysis (math.FA)
Document Type:
Fachzeitschrift
Article
File Description:
application/pdf
Language:
English
ISSN:
1099-1476
0170-4214
0170-4214
DOI:
10.1002/mma.9248
DOI:
10.48550/arxiv.2401.16493
Access URL:
Rights:
Wiley Online Library User Agreement
CC BY NC SA
CC BY NC SA
Accession Number:
edsair.doi.dedup.....6a0373e01c2003ecd19deb66f9369a44
Database:
OpenAIRE
Weitere Informationen
Let be the Catalan sequence and a linear and bounded operator on a Banach space such is a power‐bounded operator. The Catalan generating function is defined by the following Taylor series: Note that the operator is a solution of the quadratic equation . In this paper, we define powers of the Catalan generating function in terms of the Catalan triangle numbers. We obtain new formulae that involve Catalan triangle numbers: the spectrum of and the expression of for in terms of Catalan polynomials ( is the usual convolution product in sequences). In the last section, we give some particular examples to illustrate our results and some ideas to continue this research in the future.