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In this paper, we construct a self-adjoint operator T generated by thesixth-order Krall differential expression in the extended Hilbert spaceL^2(-1,1) + C^2. To obtain T, we apply a new general theory, the so-calledGKN-EM theory, developed recently by Littlejohn and Wellman that extends theclassical Glazman-Krein-Naimark theory using a complex symplectic geometricapproach developed by Everitt and Markus. This work extends earlier studies ofthe Krall expression by both Littlejohn and Loveland.

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