Event Type:

Department Colloquium

Date/Time:

Tuesday, April 20, 2004 - 05:00

Guest Speaker:

Paul DuChateau

Institution:

Colorado State University

Abstract:

Duality principles are prevalent in applied mathematics. For example, solvability of the matrix equation, Ax=b in R^n, is equivalent to uniqueness for the adjoint equation A*z=f. This is just the observation that the range of A is orthogonal to the space of A* and this assertion extends to the more general situation where A is a topological vector space isomorphism. Essentially the same observation leads to a result in control theory which asserts that a system is controllable if and only if a certain adjoint system is observable. Now we can add to these the following result: In an inverse problem in which a certain missing ingredient is to be identified from overspecified data, that ingredient is, in fact, identifiable from the data, if an associated adjoint problem is uniquely solvable. This principle will be illustrated with some examples which shed some light on the question of just how much information is needed in order to identify a given missing ingredient.