Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On volterra integral operators with highly oscillatory kernels

Language

English

Abstract

We study the high-oscillation properties of solutions to integral equations associated with two classes of Volterra integral operators: compact operators with highly oscillatory kernels that are either smooth or weakly singular, and noncompact cordial Volterra integral operators with highly oscillatory kernels. In the latter case the focus is on the dependence of the (uncountable) spectrum on the oscillation parameter. It is shown that the results derived in this paper merely open a window to a general theory of solutions of highly oscillatory Volterra integral equations, and many questions remain to be answered.

Keywords

Cordial volterra operators, Highly oscillatory kernels, Highly oscillatory solutions, Non-compact volterra operators, Spectra, Volterra integral operators

Publication Date

2014

Source Publication Title

Discrete And Continuous Dynamical Systems

Volume

34

Issue

3

Start Page

915

End Page

926

Publisher

American Institute of Mathematical Sciences

DOI

10.3934/dcds.2014.34.915

Link to Publisher's Edition

http://dx.doi.org/10.3934/dcds.2014.34.915

ISSN (print)

10780947

ISSN (electronic)

15535231

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