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Article Dans Une Revue Research in the Mathematical Sciences Année : 2022

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Résumé

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission eigenvalue problem and studied their locations. In this paper, we establish the completeness of the generalized eigenfunctions and derive an optimal upper bound for the counting function under these conditions, assuming additionally that the coefficients are twice continuously differentiable. The approach is based on the spectral theory of Hilbert-Schmidt operators.
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Dates et versions

hal-03508784 , version 1 (03-01-2022)

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Jean Fornerod, Hoai-Minh Nguyen. The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations. Research in the Mathematical Sciences , 2022, 9 (1), ⟨10.1007/s40687-021-00303-1⟩. ⟨hal-03508784⟩
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