Sturm-Liouville problems with eigendependent boundary and transmissions conditions (Q815138)

The authors study a Sturm--Liouville spectral problem on a finite interval \((a,b)\) having a discontinuity at an interior point \(x=c\), and with an eigenparameter entering both the equation and the boundary conditions at \(x=a\) and \(x=b\) and the transmission conditions at \(x=c\). They rewrite the problem as a spectral problem for some operator~\(A\) in a suitable Hilbert space that is a finite-dimensional dilation of~\(L_2(0,1)\), and then derive the asymptotics of the eigenvalues and eigenfunctions of~\(A\).