Beurling-Malliavin theory for Toeplitz kernels
Abstract
We consider the family of Toeplitz operators
T
J
S
¯
a
acting in the Hardy space
H
2
in the upper halfplane;
J
and
S
are given meromorphic inner functions, and
a
is a real parameter. In the case where the argument of
S
has a power law type behavior on the real line, we compute the critical value
c(J,S)=inf{a:ker
T
J
S
¯
a
≠0}.
The formula for
c(J,S)
generalizes the Beurling-Malliavin theorem on the radius of completeness for a system of exponentials.