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math.RA2014★ 10 cited
Rota-Baxter operators on the polynomial algebras, integration and averaging operators
Li Guo, Markus Rosenkranz, Shanghua Zheng
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…
math.RA2014★ 3 cited
Classification of Rota-Baxter operators on semigroup algebras of order two and three
Li Guo, Markus Rosenkranz, Shanghua Zheng
In this paper we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices fo…
math.RA2014★ 2 cited
Free integro-differential algebras and Gröbner-Shirshov bases
Xing Gao, Li Guo, Markus Rosenkranz
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative an…