The Solution Sets of Extremal Problems in H 1

Eric Hayashi
1985 Proceedings of the American Mathematical Society  
Let u be an essentially bounded function on the unit circle T. Let Su denote the subset of the unit sphere of H1 on which the functional F i-► f0 w u(ett)F(e't) dt/2ir attains its norm. A complete description of Su is given in terms of an inner function 60 and an outer function go in H2 for which <?q is an exposed point in the unit ball of if1. An explicit description is given for the kernel of an arbitrary Toeplitz operator on H2. The exposed points in if1 are characterized; an example is
more » ... of a strong outer function in H1 which is not exposed.
doi:10.2307/2045546 fatcat:4km35tyhpfcblailrcfdwytzeq