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Winter 2020 On the solutions of linear Volterra equations of the second kind with sum kernels
Pierre-Louis Giscard
J. Integral Equations Applications 32(4): 429-445 (Winter 2020). DOI: 10.1216/jie.2020.32.429

Abstract

We consider a linear Volterra integral equation of the second kind with a sum kernel K(t,t)=iKi(t,t) and give the solution of the equation in terms of solutions of the separate equations with kernels Ki, provided these exist. As a corollary, we obtain a novel series representation for the solution with improved convergence properties. We illustrate our results with examples, including the first known Volterra equation solved by Heun’s confluent functions. This solves a long-standing problem pertaining to the representation of such functions. The approach presented here has widespread applicability in physics via Volterra equations with degenerate kernels.

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Pierre-Louis Giscard. "On the solutions of linear Volterra equations of the second kind with sum kernels." J. Integral Equations Applications 32 (4) 429 - 445, Winter 2020. https://doi.org/10.1216/jie.2020.32.429

Information

Received: 9 September 2019; Revised: 6 January 2020; Accepted: 13 February 2020; Published: Winter 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/jie.2020.32.429

Subjects:
Primary: 45A05, 45D05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 4 • Winter 2020
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