Minimality of the system of root functions of Sturm–Liouville problems with decreasing affine boundary conditions
We consider Sturm–Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in $L_2(0,1)$, except for some cases where this system is neither complete nor minimal.