20 citations · 26 across the 5 of their papers we have counts for
6 papers
Generalized Reynolds algebras from Volterra integrals and their free construction by complete shuffle product
Li Guo, Richard Gustavson, Yunnan Li
This paper introduces algebraic structures for Volterra integral operators with separable kernels, in the style of differential algebra for derivations and Rota-Baxter algebra for…
A reduction algorithm for Volterra integral equations
Richard Gustavson, Sarah Rosen
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specif…
An algebraic study of Volterra integral equations and their operator linearity
Li Guo, Richard Gustavson, Yunnan Li
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an al…
New order bounds in differential elimination algorithms
Richard Gustavson, Alexey Ovchinnikov, Gleb Pogudin
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in t…
Effective bounds for the consistency of differential equations
Richard Gustavson, Omar León Sánchez
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated t…
New effective differential Nullstellensatz
Richard Gustavson, Marina Kondratieva, Alexey Ovchinnikov
We show new upper and lower bounds for the effective differential Nullstellensatz for differential fields of characteristic zero with several commuting derivations. Seidenberg was…