On the pseudospectra of Berezin-Toeplitz operators

Details On the pseudospectra of Berezin-Toeplitz operators On the pseudospectra of Berezin-Toeplitz operators

2003-04-15

arxiv.org/abs/math/0304182v2

Mathematics

Spectral Theory

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Scientific paper

We estimate the norm of the resolvent of non-selfadjoint Berezin Toeplitz operators in the semi-classical limit, under various assumptions on the Poisson bracket of the real and imaginary parts of the symbol. In case this bracket is negative, we symbolically construct pseudomodes well-localized in phase space. We also show that the numerical range converges to the convex hull of the image of the symbol. Our techniques involve the theory of Hermite distributions and classical subelliptic results of H\"ormander.

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