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

University course catalogue: 201.2.2051