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arXiv · 2609.16038

Study of the algebra of smooth integro-differential operators with applications

Ahmad Haghany·Adel Kassaian
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Abstract

We study the algebra of integro-differential operators with smooth coefficients and kernels on a subspace of $C^\infty[a,b]$. We find a normal form for elements of this algebra and determine its unit group. The formulation of inverses gives explicit solutions of inhomogeneous linear Volterra integro-differential equations and Volterra integral equations of first kind with smooth kernels.

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Ahmad Haghany, Adel Kassaian. 2026-09-11. Study of the algebra of smooth integro-differential operators with applications. https://doi.org/10.1142/s0219498819500099

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