Department of Mathematics
On volterra integral operators with highly oscillatory kernels
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.
Cordial volterra operators, Highly oscillatory kernels, Highly oscillatory solutions, Non-compact volterra operators, Spectra, Volterra integral operators
Source Publication Title
Discrete And Continuous Dynamical Systems
American Institute of Mathematical Sciences
Brunner, Hermann. "On volterra integral operators with highly oscillatory kernels." Discrete And Continuous Dynamical Systems 34.3 (2014): 915-926.