Green's Functions for ODEs on Large and Unbounded Intervals
Abstract: Many spectral problems are naturally posed on the infinite line. As an example, consider the linear operator $Lu=a(x)u''+b(x)u'+c(x)u$ and the spectral problem $Lu=su$. We assume that the spectral parameter $s$ is in the resolvent of the operator $L$ or is a simple eigenvalue. For numerical purposes one typically restricts the problem to a finite interval introducing a boundary operator. We study the properties of Green's functions of all-line and bounded interval problems for different boundary operators.