Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol

Tatyana Barron (1) , Xiaonan Ma (2) , George Marinescu (3) , Martin Pinsonnault (1)

1 Department of Mathematics
2 IMJ - Institut de Mathématiques de Jussieu
3 Mathematisches Institut

We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of the distance of a Toeplitz operator to the space of self-adjoint and multiplication operators.

Mots clés: Berezin-Toeplitz quantization; Dirac operator; semi-classical limit

Domaines: Géométrie différentielle [math.DG]; Géométrie symplectique [math.SG]; Physique mathématique [math-ph]

Tatyana Barron, Xiaonan Ma, George Marinescu, Martin Pinsonnault. Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol. Journal of Mathematical Physics, 2014, 55 (4), pp.042108. ⟨10.1063/1.4870869⟩. ⟨hal-00872359v2⟩