The Time Derivative
Christian Seifert, Sascha Trostorff, Marcus Waurick · Operator theory · 2021
Abstract It is the aim of this chapter to define a derivative operator on a suitable L2-space, which will be used as the derivative with respect to the temporal variable in our applications. As we want to deal with Hilbert space-valued functions, we start by introducing the concept of Bochner–Lebesgue spaces, which generalises the classical scalar-valued Lp-spaces to the Banach space-valued case.