On the singular values and eigenvalues of the Fox-Li and related operators (Q634456)

The main goal of the article is to study the singular values and eigenvalues of the Fox-Li operators: \((F_{\omega } f)\left(x\right)=\int _{-1}^{1}e^{i\omega \left(x-y\right)^{2} } f\left(y\right)dy,\quad x\in (-1,\; 1) \), as a bounded operator on \(L^{2} \left(-1,\; 1\right)\). The authors use Wiener-Hopf theory for convolution type operators and show how this theory can be used to obtain insight into the behavior of the singular values of the Fox-Li operator. The results of this article have much interest for investigators in laser and maser engineering and other fields where operators with high oscillation are used.