Differential Triplets on Hilbert Spaces

In the theory of differential operators acting on functions of the one variable, \(\frac {\mathrm {d}}{\mathrm {d}x}\) is the building block. We may supplement \(\frac {\mathrm {d}}{\mathrm {d}x}\) with homogeneous linear boundary conditions, construct higher-order differential operators (as the Laplace operator), study the properties of these operators (invertibility, closedness), and consider their adjoint operator. Also various differential equations may be investigated.