Szego Seminar: "A Functional Decomposition of Finite Bandwidth Reproducing Kernel Hilbert Spaces"

Abstract: In this talk, we consider a particular class of analytic reproducing kernels, called finite bandwidth kernels, that give rise to Hilbert spaces of analytic functions on the unit disk. These kernels have matrix representations with a finite number of non-zero diagonals. In particular, we will discuss the tridiagonal case and a specific family of spaces studied by Adams and McGuire. Notably, in this setting one can obtain an explicit functional decomposition of the space that clarifies its relation to the classical Hardy space. Time permitting, we will discuss how some of these results generalize to higher bandwidth spaces.

Host: Christopher Felder