The sharp form of the strong Szegő theorem
The sharp form of the strong Szegő theorem
Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the strong Szeg\H{o} theorem says that for any real-valued $L$ on the unit circle …