We are concerned here with the transmission eigenvalues connected with a degerenate boundary problem involving a 2x2 system of differential operators. By a transmission eigenvalue of the boundary problem we mean a non-zero eigenvalue with the property that each component of a corresponding eigenvector is non-trivial. To derive information concerning the transmission eigenvalues, we proceed in the following way. Firstly we show that the Hilbert space operator induced by the boundary problem is just the linearization of a quadratic operator pencil which is parameter-elliptic. Then by utilizing some known facts concerning this pencil as well as some results pertaining to the uniqueness of the Cauchy problem, we are able to characterize the transmission eoigenvalues.


Melvin Faierman

Research Area



Tue, 20/08/2013 - 12:00pm to 1:00pm


RC-4082, Red Centre Building, UNSW