Colloquium

Abstract

We present in this talk a generalization toL^p spaces of the unit circle of the Adamjan Arov Kreintheory on uniform meromorphic approximation. Moreprecisely, we will see that the n-th singular numberof some suitably defined Hankel operator with symbolf does express the distance of f to B_n^-1 H^p, where H^p is the familiar Hardyspace and B_n the set of Blaschke product of degreeat most n; if moreover p is at least 2, singular vectorsdefined through Hammerstein type equations allows oneto express the error function. Our approach istopological, associating to singular vectors andvalues certain critical points of the Hankel quadraticform on the unit sphere of the Hardy space.Subsequently, we shall discuss Morse-type inequalitiesfor these critical points as well as non-Hermitianorthogonality relations arising from the properties ofSchmidt pairs in this context.