Generalized Riordan groups and operators on polynomials

Shaul Zemel

doi:10.1016/j.laa.2016.01.021

Generalized Riordan groups and operators on polynomials

Shaul Zemel^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups arising from different weights are isomorphic since they are conjugate. We also prove a result about the intersection of two generalized Riordan groups with different weights.

Original language	English
Pages (from-to)	286-308
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	494
DOIs	https://doi.org/10.1016/j.laa.2016.01.021
State	Published - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc. All rights reserved.

Keywords

Functionals on polynomials
Infinite matrices
Polynomial sequences
Riordan arrays

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10.1016/j.laa.2016.01.021

Cite this

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abstract = "We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups arising from different weights are isomorphic since they are conjugate. We also prove a result about the intersection of two generalized Riordan groups with different weights.",

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AB - We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups arising from different weights are isomorphic since they are conjugate. We also prove a result about the intersection of two generalized Riordan groups with different weights.

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KW - Infinite matrices

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ER -

Generalized Riordan groups and operators on polynomials

Abstract

Bibliographical note

Keywords

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