On the asymptotic expansion of Bergman kernel

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We study the asymptotic of the Bergman kernel of the spin c Dirac operator on high tensor powers of a line bundle.

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Generalized Bergman kernels on symplectic manifolds (2004, methodology): “In [18], we also focused on the full off-diagonal asymptotic expansion (cf.”
Exponential estimate for the asymptotics of Bergman kernels (2013, methodology): “…/µ 0 , we have From Lemma 1.3, (2.3) and (2.4), for any u 0 > 0 , m ∈ N , there exists and that for u u 0 , p 2 C L /µ 0 , x, x ′ ∈ X , we have (cid:12) (cid:12) To obtain (2.1) and (2.2) in general, we proceed as in the proof of [6, Theorem 4.11] and [3, Theorem 11.14] (cf. [15, Theorem 4.2.5] ).”
Number Variance of Random Zeros on Complex Manifolds (2006, background): “(See also [ DLM , MM] for off-diagonal exponential estimates in a more general setting.) We do not need Agmon estimates for this paper; instead Theorem 2.4 suffices.”