On the invertibility of the operator d/dt + A in certain functional spaces - Gorodnii, M. F. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
We prove that the operator ddt + A constructed on the basis of a sectorial operator A with spectrum in the right half-plane of ℂ is continuously invertible in the Sobolev spaces W_p^1 (ℝ, D_α), α ≥ 0. Here, D_α is the domain of definition of the operator A^α and the norm in D_α is the norm of the graph of A^α.