Plan of the mini-course
1. Basics
- Discrete and continuous realisations
- Examples: the Carleman operator, the Hilbert matrix.
- Hardy space realisations.
- Positivity and connection with the moments sequences.
- Bounded Hankel operators, Nehari's theorem.
- Finite rank Hankel operators, Kronecker's theorem.
- Compact Hankel operators, Hartman's theorem.
2. Optional topics:
- Trace class Hankel operators, the theorem of Peller-Coifman-Rochberg.
- Howland's work, analogy with the Schrödinger operator.
- The Adamyan-Arov-Krein theorem, rational approximation, asymptotics of
eigenvalues of Hankel operators.
- Hankel operators with piecewise continuous symbols; essential spectrum.
- Periodic Hankel operators (my recent work with Sobolev)
- Inverse problems for Hankel operators.