Quantization formula for symplectic manifolds with boundary (Q1305435)

In the paper under review the authors extend their previous result [Invent. Math. 132, 229-259, (1998; Zbl 0944.53047)] to the case of symplectic manifolds with boundary. They also give a general quantization formula that works for both regular and singular reduction. As simple applications they obtain analytic versions of the relative residue formula of Guillemin and Kalkman as well was a Guillemin-Sternberg type formula for singular reductions under circle actions.