Patrick Gerard (Orsay)

An inverse spectral problem for pairs of Hankel operators on the circle

I will review recent results allowing to describe the symbol of a compact Hankel operator on the circle in terms of the singular values of this operator and of the associated shifted operator. I will also present more recent partial generalizations to the case of non compact Hankel operators. Finally I will explain how this problem is connected to some integrable Hamiltonian dynamics on the Hardy space. This talk is from joint works with Sandrine Grellier and Alexander Pushnitski.