Advanced topics in complex variables

Course topics

  • Some review of complex variables
  • Hilbert spaces of analytic functions. General theory
  • Bergman space
  • Hardy spaces
  • Fractional Hardy space and self similar systems
  • Bargmann-Fock space and second quantization
  • Banach spaces of analytic functions.
  • Frechet spaces and Schwartz spaces
  • Proof of Riemann’s mapping theorem
  • Dual of the space of functions analytic in a given open set
  • Gelfand triples and applications

Course Information

University course catalogue:
201.2.2051
Level:
Graduate
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