Abstract
We explain the construction of a Hilbert space on quadrics arising by the method of pairing polarizations. Then we introduce a family of measures and operators from function spaces on these quadrics to L2(Sn) which are defined by fiber integration. We compare the quantization operators and characterize them in the framework of pseudo-differential operator theory. An asymptotic property of the reproducing kernel of the Hilbert spaces consisting of holomorphic functions defined on quadrics is proved. This is a generalization of the Segal-Bargmann space and its reproducing kernel. Next we treat the case of the complex projective space and we explain that the space corresponding to the quadric is a matrix space consisting of rank-one complex matrices whose square is zero. Most of the theorems can be stated in the same way parallel to the sphere case.
