On the singular values and eigenvalues of the Fox-Li and related operators

Albrecht Böttcher*, Hermann Brunner, Arieh Iserles, Syvert P. Nørsett

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

14 Citations (Scopus)


The Fox-Li operator is a convolution operator over a finite interval with a special highly oscillatory kernel. It plays an important role in laser engineering. However, the mathematical analysis of its spectrum is still rather incomplete. In this expository paper we survey part of the state of the art, and our emphasis is on showing how standard Wiener-Hopf theory can be used to obtain insight into the behaviour of the singular values of the Fox-Li operator. In addition, several approximations to the spectrum of the Fox-Li operator are discussed and results on the singular values and eigenvalues of certain related operators are derived.

Original languageEnglish
Pages (from-to)539-561
Number of pages23
JournalNew York Journal of Mathematics
Publication statusPublished - Dec 2010

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Fox–Li operator
  • Wiener–Hopf operator
  • oscillatory kernel
  • eigenvalue
  • singular value


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