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arXiv · 2309.00603

Regular singular Volterra equations on complex domains

Veronica Fantini·Aaron Fenyes
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Abstract

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, especially when the Volterra equation extends to a complex domain. Our main result is to show that for a certain kind of regular singular Volterra equation on a complex domain, there is always a unique solution of a certain form. As a motivating example, this kind of Volterra equation arises when using Laplace transform methods to solve a level 1 differential equation.

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Veronica Fantini, Aaron Fenyes. 2023-09-01. Regular singular Volterra equations on complex domains. https://doi.org/10.1137/23m1613876

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