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

Shanghua Zheng, Li Guo, Markus Rosenkranz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The concept of a Rota-Baxter operator is 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.

Original languageEnglish (US)
Pages (from-to)481-507
Number of pages27
JournalPacific Journal of Mathematics
Volume275
Issue number2
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Averaging operator
  • Integration
  • Monomial linear operator
  • Rota-Baxter operator

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