Quantization Formula for Symplectic Manifolds with Boundary. Revised Version

摘要

We extend or earlier work in (TZ1), where an analytic approach to the Guillemin-211u001eSternberg geometric quantization conjecture (GuS) was developed, to the case of 211u001emanifolds with boundary. We also give a general quantization formula that works 211u001efor both regular and singular reductions. As simple applications, we prove an 211u001eanalytic analogue of the relative residue formula of Guillemin-Kalkman (GuK) and 211u001eMartin (M), as well as a Guillemin-Sternberg type formula for singular reductions 211u001eunder circle actions.