Let L be the Sturm–Liouville operator, a linear differential operator of the form L = d d x [ p ( x ) d d x ] + q ( x ) and let D be the vector-valued boundary conditions operator D u = [ α α 1 u ′ ( 0 ) + β β 1 u ( 0 ) α α 2 u ′ ( ℓ ℓ ) + β β 2 u ( ℓ ℓ ) ] .