A New Spectral Analysis of the Sixth-order Krall Differential Expression

Abstract: In this paper, we construct a self-adjoint operator T generated by the sixth-order Krall differential expression in the extended Hilbert space L^2(-1,1) + C^2. To obtain T, we apply a new general theory, the so-called GKN-EM theory, developed recently by Littlejohn and Wellman that extends the classical Glazman-Krein-Naimark theory using a complex symplectic geometric approach developed by Everitt and Markus. This work extends earlier studies of the Krall expression by both Littlejohn and Loveland.