Title: The Jacobi operator and its Weyl--Titchmarsh--Kodaira $m$-functions
Speaker: Jonathan Stanfill (Baylor University)
Abstract: We discuss the Jacobi differential operator and its associated Weyl--Titchmarsh--Kodaira $m$-functions utilizing generalized boundary values for singular Sturm--Liouville operators. Weyl $m$-functions for the Jacobi differential operator with separated boundary conditions will be constructed. While general solutions of the Jacobi differential equation we consider are given by $2F1$ hypergeometric functions, of particular interest will be the boundary conditions that lead to the Jacobi polynomial solutions for different choices of parameters. These polynomial solutions will also include Gegenbauer, Legendre, and Chebyshev orthogonal polynomials as special cases.
This talk is based on joint work with Fritz Gesztesy and Mateusz Piorkowski.