Schur's Algorithm and the Carathéodory --Toeplitz TheoremThe original mathematical importance of positive definite Toeplitz matrices is in the solution of the classical Carathéodory coefficient problem, proved independently by Toeplitz and Carathéodory in 1911. An analytic mapping of the unit disk |z|<1 into the closed right half-plane is said to be a Carathéodory function, or a function in the class C. In 1917, Schur gave a constructive proof of the Ca
