Dendriform Equations
Kurusch Ebrahimi-Fard, Dominique Manchon
TL;DR
This paper explores solutions to specific linear equations within dendriform algebras, highlighting their connections to Rota-Baxter operators and applications like integrals.
Contribution
It introduces methods for solving dendriform equations and links these solutions to classical integral operators, expanding the algebraic framework.
Findings
Established solution techniques for dendriform equations
Linked dendriform structures to Rota-Baxter operators
Demonstrated applications in integral calculus
Abstract
We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota-Baxter operators, e.g. the Riemann integral or Jackson's q-integral.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Holomorphic and Operator Theory