Rota–Baxter operators on the polynomial algebra, integration, and averaging operators

2014/07/20 by Li Guo, Markus Rosenkranz, Shanghua Zheng
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Holomorphic and Operator Theory #Linear operators #Matrix Theory and Algorithms #Monomial #Monomial basis #Operator theory #Polynomial #math.AC #math.CA #math.RA #msc:12H20 #msc:16W99 #msc:45N05 #msc:47G10

paper · pdf · doi:10.2140/pjm.2015.275.481

published as Pacific J. Math. 275 (2015) 481-507 · 20 pages

arxiv created 2014/07/20 · openalex publication_date 2015/05/15 · arxiv updated 2016/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra k[x]. We consider two classes of Rota-Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota-Baxter operators. For the second class, we make use of the double product on Rota-Baxter algebras.

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