On Volterra integral operators with highly oscillatory kernels

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6 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)915-929
Number of pages15
JournalDiscrete and Continuous Dynamical Systems - Series A
Volume34
Issue number3
DOIs
Publication statusPublished - Mar 2014

Keywords

  • Volterra integral operators
  • highly oscillatory kernels
  • non-compact Volterra operators
  • cordial Volterra operators
  • spectra
  • highly oscillatory solutions

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