I figured it out!
I showed that the norm induced by \langle \cdot, \cdot \rangle_{\alpha} is indeed equivalent to the standard Sobolev norm \Vert \cdot \Vert_{W^{2,2}} of the Sobolev space W^{2,2} which is of course the (reproducing kernel) Hilbert space H^2 .
Hello everybody,
I am given a "Sobolev type innerproduct"
\langle f,g \rangle_{\alpha} = \langle f,g \rangle_{L^2} + \alpha \langle Rf,Rg \rangle_{L^2}
for some \alpha \geq 0 and R some differential operator (e.g. the second-derivative operator).
My question is now whether a function...