Inverse Problems, Adjoints and Identifiability

Duality principles are prevalent in applied mathematics.For example, in
Rn, solvability of a matrix equation is equivalent to uniqueness for the
adjoint equation. In control theory, a system is controllable if and
only if a certain adjoint system is observable. Now we can add the
following result: In an inverse problem in which a certain missing
ingredient is to be identified, that ingredient is, in fact,
identifiable from the specified data, if an associated adjoint problem
is uniquely solvable. This principle will be illustrated with some
examples.