Spectral analysis of the discrete Maxwell operator: The limiting absorption principle

Olivier Poisson

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arXiv · 2310.04067

Spectral analysis of the discrete Maxwell operator: The limiting absorption principle

Olivier Poisson

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Abstract

We are interested by the spectral analysis of the anisotropic discrete Maxwell operator $\hat H^D$ defined on the square lattice $\rm Z\!\!\! Z^3$. In aim to prove that the limiting absorption principle holds we construct a conjugate operator to the Fourier series of $\hat H^D$ at any not-zero real value. In addition we show that at some particular thresholds the conjugate operator is essentially self-adjoint.

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Olivier Poisson. 2023-10-06. Spectral analysis of the discrete Maxwell operator: The limiting absorption principle. https://arxiv.org/abs/2310.04067

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