Overview
This course focuses on the Hilbert matrix operator on Bergman-type spaces. By the end of the course, learners will be able to understand and apply the Hilbert matrix on various function spaces, including Hardy, mixed norm, weighted Bergman, Dirichlet, Hardy-Bloch, Besov, and generalized mixed norm spaces. The course teaches skills in analyzing and manipulating Hilbert matrices in the context of different function spaces. The teaching method involves theoretical explanations and practical examples. This course is intended for individuals interested in functional analysis, operator theory, and analytic function spaces.
Syllabus
Intro
The Hilbert matrix
Hilbert matrix on spaces of holomorphic functions
Hardy and mixed norm spaces
Weighted Bergman and Dirichlet spaces
Hardy-Bloch and Besov spaces
Hilbert matrix on Hardy spaces
Hilbert matrix on Bergman spaces (1)
Hilbert matrix on generalized mixed norm spaces (II)
Hilbert matrix on weighted Bergman spaces (V)
Generalized Hilbert matrix
Taught by
Fields Institute