Diagonalization of elliptic systems via pseudodifferential projections

نویسندگان

چکیده

Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. Relying basis projections commuting with A, we construct almost-unitary that diagonalizes modulo infinitely smoothing operator. We provide invariant algorithm for the computation its full symbol, as well explicit formula subprincipal symbol. Finally, give quantitative description relation between spectrum and approximate diagonalization, discuss implications at level spectral asymptotics.

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ژورنال

عنوان ژورنال: Journal of Differential Equations

سال: 2022

ISSN: ['1090-2732', '0022-0396']

DOI: https://doi.org/10.1016/j.jde.2021.12.032