Identifiability of Linear Systems in Hilbert Spaces

The identifiability problem is discussed for linear dynamical systems described by first and second order evolution equations in Hilbert spaces. The unknowns are the initial values and the operators appearing in the system equations and a number of identifiability conditions are established within the framework of linear operator theory. These are applied to various classes of partial differential equations on bounded and unbounded spatial domains to obtain the constant and spatially varying parameter identifiability conditions for such systems.