The Szego Theorem for multiplicative Toeplitz matrices

Professor Alexander Pushnitski (KCL) will present his research in Analysis.

The classical (additive) Toeplitz matrices are infinite matrices of the form {a(n-m)}, where a is a function on the set of integers. The multiplicative Toeplitz matrices are infinite matrices of the form {a(n/m)}, where a is a function on the set of positive rationals. At the first sight, the latter looks like a strange and artificial definition. In fact, multiplicative Toeplitz matrices appeared in the work by O.Toeplitz of 1938 in connection with the theory of Dirichlet series! I will try to motivate this definition. Furthermore, I will recall the classical Szego theorem for additive Toeplitz matrices and discuss its multiplicative analogue. This is joint work with Nikolai Nikolski (Bordeaux).