Minimality of the system of root functions of Sturm–Liouville problems with decreasing affine boundary conditions
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 147-162
MSC: 34B24, 34L10.
DOI: 10.4064/cm109-1-12
Abstract
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.
