Differentiable functions and the generators on a Hilbert-Lie group
It is well-known that the domain of a generator of a convolution semigroup on a finite-dimensional Lie group \(G\) contains the space \(C_2(G)\) of all twice continuously left differentiable functions \(f\) with \(\| Df \|_\infty <\infty\) and \(\| D^2f\|_\infty <\infty\). This result is extended to Hilbert-Lie groups by showing that here generators contain all functions in \(C_2(G)\) which depend on finitely many canonical coordinates only.
scientific article; zbMATH DE number 1208041