JournalsowrVol. 14, No. 4pp. 2943–2985

Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures

  • David Damanik

    Rice University, Houston, USA
  • Fritz Gesztesy

    Baylor University, Waco, USA
  • Peter Yuditskii

    Johannes Kepler University Linz, Austria
Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures cover

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Abstract

Reflectionless operators in one dimension are particularly amenable to inverse scattering and are intimately related to integrable systems like KdV and Toda. Recent work has indicated a strong (but not equivalent) relationship between reflectionless operators and almost periodic potentials with absolutely continuous spectrum. This makes the realm of reflectionless operators a natural place to begin addressing Deift’s conjecture on integrable flows with almost periodic initial conditions and Simon’s conjecture on gems of spectral theory establishing correspondences between certain coefficient and spectral properties.

Cite this article

David Damanik, Fritz Gesztesy, Peter Yuditskii, Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures. Oberwolfach Rep. 14 (2018), no. 4, pp. 2943–2985

DOI 10.4171/OWR/2017/49