Spectral properties of Sturm-Liouville equations with singular energy-dependent potentials (Q2877324)

The author studies spectral properties of the Dirichlet problem (or a problem with more complicated boundary conditions involving the quasi-derivative) for the equation NEWLINE\[NEWLINE -y''+qy+2\lambda py=\lambda^2 y, NEWLINE\]NEWLINE where \(p\) is a real-valued function from \(L_2(0,1)\), \(q\) is a real-valued distribution from the Sobolev space \(W_2^{-1}(0,1)\), \(\lambda \in \mathbb C\), is the spectral parameter. This spectral problem is linearized in a certain Pontryagin space. The notion of norming constants is introduced for this situation. Sufficient conditions are found for the spectrum to be real and simple.