Abstract
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 language | English |
|---|---|
| Pages (from-to) | 539-561 |
| Number of pages | 23 |
| Journal | New York Journal of Mathematics |
| Volume | 16 |
| Publication status | Published - Dec 2010 |
Scopus Subject Areas
- Mathematics(all)
User-Defined Keywords
- Fox–Li operator
- Wiener–Hopf operator
- oscillatory kernel
- eigenvalue
- singular value