The Absolute Continuity of Toeplitz's Matrices

摘要

This formula appears in the work [2] of Calderon, Spitzer, and Widom. However, we shall offer a different derivation, one that points out an interesting connection between T and the Szego kernel function. Next we shall a result from the Aronszajn-Donoghue [1] theory of exponential representations of analytic functions, and consequently deduce that Y is absolutely continuous. We conclude with section 4 where 1.2 is generalized.