Explore the Hilbert matrix operator and its applications in various analytic function spaces in this 54-minute lecture by Boban Karapetrovic from the University of Belgrade. Delve into the properties of the Hilbert matrix on spaces of holomorphic functions, including Hardy, mixed norm, weighted Bergman, and Dirichlet spaces. Examine the operator's behavior on Hardy-Bloch and Besov spaces, and investigate its characteristics on generalized mixed norm and weighted Bergman spaces. Gain insights into the generalized Hilbert matrix and its significance in the field of analytic function theory.