# $L^p$-bounds for eigenfunctions of analytic non-self-adjoint operators with double characteristics

@inproceedings{White2021LpboundsFE, title={\$L^p\$-bounds for eigenfunctions of analytic non-self-adjoint operators with double characteristics}, author={Francis White}, year={2021} }

We prove sharp uniform L-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators P on R whose principal symbols are doubly-characteristic at the origin of R. Our bounds hold under two main assumptions on P : (1) the total symbol of P extends holomorphically to a tubular neighborhood of R in C, and (2) the quadratic approximation to the principal symbol of P at the origin is elliptic along its singular space. Most notably, our assumptions on the…

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