An algebraic study of Volterra integral equations and their operator linearity

DOI10.1016/j.jalgebra.2021.12.025zbMath1489.16046arXiv2008.06756OpenAlexW3048974664MaRDI QIDQ2068184

Richard Gustavson, Yunnan Li, Li Guo

Publication date: 19 January 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.06756

zbMATH Keywords

integral equationVolterra operatordifferential algebrarooted treesVolterra equationiterated integralRota-Baxter algebraoperated algebralinearity of integral equation

Mathematics Subject Classification ID

Trees (05C05) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Integral operators (45P05) Differential algebra (12H05) Volterra integral equations (45D05) Abstract integral equations, integral equations in abstract spaces (45N05) Associative rings and algebras with additional structure (16W99) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (9)

Hopf algebra of multidecorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases ⋮ Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects ⋮ Construction of free commutative Reynolds algebras by Gröbner-Shirshov bases ⋮ Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases ⋮ Compatible structures of nonsymmetric operads, Manin products and Koszul duality ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Reynolds algebras and their free objects from bracketed words and rooted trees ⋮ Matching Rota-Baxter BiHom-algebras and related algebraic structures

Cites Work

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• On integro-differential algebras.
• Free integro-differential algebras and Gröbner-Shirshov bases.
• An analytic problem whose solution follows from a simple algebraic identity
• Renormalisation and locality: branched zeta values
• Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
• Operated semigroups, Motzkin paths and rooted trees
• Hopf algebras, renormalization and noncommutative geometry
• Analytical approximations and Padé approximants for Volterra's population model
• Algebraic renormalisation of regularity structures
• The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
• Gian-Carlo Rota on analysis and probability. Selected papers and commentaries. Edited by Jean Dhombres, Joseph P. S. Kung and Norton Starr
• Reynolds algebras and their free objects from bracketed words and rooted trees
• Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras
• Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
• Iterated integrals of differential forms and loop space homology
• Associative differential operations
• Algebraic structures on typed decorated rooted trees
• Iterated path integrals
• On Symbolic Approaches to Integro-Differential Equations
• CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES
• Derivation and double shuffle relations for multiple zeta values
• Baxter algebras and combinatorial identities. I
• Chen's iterated integral represents the operator product expansion

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