Positive kernels and quantization

In this paper, we investigate a method of quantization based on the concept of positive definite kernels on a principal GG-bundle with compact structural group GG. For G=U(1)G=U(1), our approach leads to Kostant–Souriau geometric quantization as well as to the coherent state method of quantization. So, the theory proposed here can be treated as a generalization of both mentioned quantizations to the case of a general compact group.