Generalized Riordan groups and operators on polynomials

Shaul Zemel

doi:https://doi.org/10.1016/j.laa.2016.01.021

Generalized Riordan groups and operators on polynomials

Shaul Zemel

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

Keywords

Functionals on polynomials
Infinite matrices
Polynomial sequences
Riordan arrays

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.laa.2016.01.021

Cite this

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title = "Generalized Riordan groups and operators on polynomials",

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.",

keywords = "Functionals on polynomials, Infinite matrices, Polynomial sequences, Riordan arrays",

author = "Shaul Zemel",

year = "2016",

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doi = "https://doi.org/10.1016/j.laa.2016.01.021",

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journal = "Linear Algebra and Its Applications",

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T1 - Generalized Riordan groups and operators on polynomials

AU - Zemel, Shaul

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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.

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.

KW - Functionals on polynomials

KW - Infinite matrices

KW - Polynomial sequences

KW - Riordan arrays

UR - http://www.scopus.com/inward/record.url?scp=84955483394&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.laa.2016.01.021

DO - https://doi.org/10.1016/j.laa.2016.01.021

M3 - مقالة

SN - 0024-3795

VL - 494

SP - 286

EP - 308

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Generalized Riordan groups and operators on polynomials

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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