The UTC Graduate School is pleased to announce that Caleb Beckler will present Master’s research titled, On the Parametrization of Self-adjoint Extensions of Singular Sturm-Liouville Operators on 03/05/2026 at 12:30 in Lupton 302. Everyone is invited to attend.
Mathematics
Chair: Roger Nichols
Co-Chair:
Abstract:
The self-adjoint extensions of a lower semi-bounded minimal Sturm-Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Plucker identity, we find the relation between self-adjoint extensions for two different parametrizations.