Abstract
Volterra equations involve integrals with a variable upper limit. In the first part of this chapter we examine the implications of Fredholm theory for Volterra equations of the second kind, and in particular we show that a Volterra integral operator has no eigenvalue except possibly zero. Usually zero is not an eigenvalue either, so Volterra operators are usually invertible. That is, equations of the first kind have solutions too.
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© 1991 Springer Science+Business Media New York
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Pipkin, A.C. (1991). Volterra Equations. In: A Course on Integral Equations. Texts in Applied Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4446-2_5
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DOI: https://doi.org/10.1007/978-1-4612-4446-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8773-5
Online ISBN: 978-1-4612-4446-2
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