… other hand, in the holomorphic setting, in [19], Christ (and Lindholm in [25]) proved an Agmon
type estimate for the Szegö kernel on C1, but they did not treat the asymptotic expansions. In
this paper, we establish the full off-diagonal asymptotic expansion and Agmon estimate for the
Bergman kernel of the spinc Dirac operator associated to high powers of an ample line bundle
in the general context of symplectic manifolds and orbifolds (Cf. Theorem 4.18; note the
important factors on the right-hand side of the estimate (4.119) which make our estimate uniform …

… In this Note, we study the asymptotic expansion of Bergman kernel for high powers of an
ample line bundle in the more general context of symplectic manifolds and orbifolds. We
also study the asymptotic expansion of the corresponding heat kernel and relates it to that of
the Bergman kernel. One of our motivations is to extend Donaldson’s recent work to
orbifolds. … We also have the following large p asymptotic expansion for the heat kernel. …