Title: A Characterization of Lower Semiboundedness for the Friedrichs Extension of Four-Coefficient Sturm–Liouville Operators
Speaker: Roger Nichols (The University of Tennessee at Chattanooga)
Speaker's URL: https://sites.google.com/mocs.utc.edu/rogernicholshomepage/home
Abstract: Using the variational characterization of the smallest eigenvalue below the essential spectrum of a lower semibounded self-adjoint operator, we prove strict domain monotonicity (with respect to changing the finite interval length) of the principal eigenvalue of the Friedrichs extension $T_F$ of the minimal operator for regular four-coefficient Sturm–Liouville differential expressions. As a consequence of the strict domain monotonicity of the principal eigenvalue of the Friedrichs extension in the regular case, and on the basis of oscillation theory in the singular context, in our main result we characterize all lower bounds of $T_F$ as those $\lambda\in \mathbb{R}$ for which the differential equation $\tau u = \lambda u$ has a strictly positive solution $u > 0$ on $(a,b)$.
URL associated with Seminar: https://u.osu.edu/aots/
