Physics – Mathematical Physics
Scientific paper
2010-07-03
Physics
Mathematical Physics
Scientific paper
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trace class case, the generic existence of transmission eigenvalues is established.
Hitrik Michael
Krupchyk Katsiaryna
Ola Petri
Päivärinta Lassi
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