The PDEs and Applications seminar: Boundedness of Schrödinger Integral Operators in Sobolev Spaces

  • Date: –12:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Anders Israelsson
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Abstract: Schrödinger integral operators (SIO) are a type of oscillatory integral operators that arise naturally in the analysis of linear partial differential equations of Schrödinger type. Hence, if one wants to say something about the regularity of the solution to a PDE of Schrödinger type, then it is enough to investigate the corresponding SIO. Until a couple of years ago not much was known about the regularity of SIO's, but as a new Littlewood-Paley type decomposition was developed the Sobolev space regularity problem was fully solved. In this talk I will sketch the proof of this and mention some of the immediate consequences.