Toeplitz matrices $A_{n}(f)$ is defined as:
$A_{n}(f)_{i,j}=c_{i-j}$ $0\leq i,j \leq n-1$, where $c_{k}$ are Fourier Coefficients of $f(\theta)=\sum_{k=- \infty}^{+\infty}c_{k}e^{\iota k \theta }$
$n$ here is the order of matrix $A_{n}(f)$.
Szegos Limit Theorems talk about determinants of large Toeplitz matrices. I am here concerned with the first Szegos limit theorem which states that: \begin{equation} lim_{n\rightarrow\infty}\frac{Det(A_{n}(f))}{Det(A_{n-1}(f))}=exp\{\frac{1}{2\pi}\int_{0}^{2\pi}log(f(\theta))d \theta\}\tag{1} \end{equation} The Wikipedia article discusses this theorem for $f$ being a non-negative valued function. I am looking for a generalisation of this theorem for $f$ being a complex-valued function. I tried searching the web but could not find a good reference. I am looking for a good reference for Szego's Limit theorems for these complex-valued $f$.
Thank you