## 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