An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line

2022/02/08 by Patrick D. Gerard, Gérard, Patrick, Alexander Pushnitski +1
Mathematics · #35F20 #47B35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2202.03783

openalex publication_date 2022/02/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We construct inverse spectral theory for finite rank Hankel operators acting on the Hardy space of the upper half-plane. A particular feature of our theory is that we completely characterise the set of spectral data. As an application of this theory, we prove the genericity of turbulent solutions of the cubic Szegő equation on the real line.

Related

• The cubic szego equation and hankel operators
• An inverse spectral problem for non-compact Hankel operators with simple spectrum
• Multiple singular values of Hankel operators
• Explicit formula for the solution of the Szegö equation on the real line and applications
• An explicit formula for the cubic Szegö equation