We study the spectrum of the Kohn Laplacian t b on the Rossi example (S 3 , L t ).In particular we show that 0 is in the essential spectrum of t b , which yields another proof of the global non-embeddability of the Rossi example.2010 Mathematics Subject Classification. Primary 32V30; Secondary 32V05.

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Let (M, g) be a smooth, compact, Riemannian manifold and {φ h } a sequence of L 2 -normalized Laplace eigenfunctions on M . For a smooth submanifold H ⊂ M , we consider the growth of the restricted eigenfunctions φ h | H by testing them against a sequence of functions {ψ h } on H whose wavefront set avoids S * H. That is, we study what we call the generalized Fourier coefficients: φ h , ψ h L 2 (H) . We give an explicit bound on these coefficients depending on how the defect measures for the two collections of functions φ h and ψ h relate. This allows us to get a little−o improvement whenever the collection of recurrent directions over the wavefront set of ψ h is small. To obtain our estimates, we utilize geodesic beam techniques.

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