Sturm–Liouville problem with a distributed condition

A special problem for the standard liner differential equation of $2$-nd order on $[0,1]$ is investigated when one of boundary conditions must be orthogonal to a given measure on $[0,1]$. The measure and the potential are complex-valued. The main theorem yields some conditions for the alternative: the codimension or the linear span of the root functions in $C[0,1]$ is either $1$ or $\infty$. The transformation operators are applied to reduce the problem to the theory of entire functions.