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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive