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- W3142041609 abstract "Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of $A$ decomposes, up to an error with superpolynomial decay, into $m$ distinct series, each associated with one of the eigenvalues of the principal symbol of $A$. These spectral results are then applied to the study of propagation of singularities in hyperbolic systems. The key technical ingredient is the use of the carefully devised pseudodifferential projections introduced in the first part of this work, which decompose $L^2(M)$ into almost-orthogonal almost-invariant subspaces under the action of both $A$ and the hyperbolic evolution." @default.
- W3142041609 created "2021-04-13" @default.
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- W3142041609 date "2021-03-26" @default.
- W3142041609 modified "2023-09-27" @default.
- W3142041609 title "Invariant subspaces of elliptic systems II: spectral theory" @default.
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