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- W2512852043 abstract "We seek to extend work by Christianson-Hassell-Toth cite{CHT} on restrictions of Neumann data of Laplacian eigenfunctions to interior hypersurfaces to a general semiclassical setting. In the semiclassical regime the appropriate generalisation is to study the restrictions of the function $v=nu(x,hD)u$ where $nu(x,hD)$ is the operator defined by quantising the normal velocity observable. For the Laplacian $nu(x,hD)=frac{1}{2}hD_{nu}$ where $nu$ is the normal to the hypersurface. We find that $||nu(x,hD)u||_{L^{2}(H)}lesssim||u||_{L^{2}(M)}$ provided $u$ is an $O_{L^{2}}(h)$ quasimode of the semiclassical pseudodifferential operator $p(x,hD)$. This statement should be interpreted as a statement of non-concentration for the quantisation of normal velocity." @default.
- W2512852043 created "2016-09-16" @default.
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- W2512852043 date "2014-03-26" @default.
- W2512852043 modified "2023-09-27" @default.
- W2512852043 title "The quantisation of normal velocity does not concentrate on hypersurfaces" @default.
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