Spectral properties of semi-classical Toeplitz operators (Q2417736)

This nice article establishes an asymptotic expansion as $\hbar\to0$ for the spectral measure of a semi-classical Toeplitz operator $Q_{\hbar}$. The reader may consult the books [\textit{L. Boutet de Monvel} and the author, The spectral theory of Toeplitz operators. Princeton, NJ: Princeton University Press (1981; Zbl 0469.47021)] and [the author and \textit{S. Sternberg}, Semi-classical analysis. Somerville, MA: International Press (2013; Zbl 1298.58001)] for introductions to Toeplitz operators and semi-classical analysis respectively. \par The article also contains a $T$-equivariant version of the above result, when it is assumed an action of a torus $T$ on the compact manifold satisfying certain conditions. As an application, the authors prove that the symbol of a Toeplitz operator is determined by the equivariant spectrum on toric varieties. For the entire collection see [Zbl 1412.22001].