For odd degree splines, with degree $k$ I know they minimize an energy:
$$E[u] = \int_{a}^{b} \left\|\frac{d^{(k+1)/2}u}{dx^{(k+1)/2}}(x)\right\|^2 \, dx, \, u(x_i) = f(x_i), \, \frac{d^l u}{dx^l}(c) = 0, \, c\in\{a,b\},$$
for sufficiently many derivatives $l$ on the boundary. Is there an analogue of the above for even degree splines. Surely those minimize something? However when I tried to derive this, the skew-adjoint operator $\frac{d^{k+1}}{dx^{k+1}}$ got in the way.
Is there a discussion of this fact in the literature?