  We study determinantal point processes on $\mathbb{C}$ induced by the
reproducing kernels of generalized Fock spaces as well as those on the unit
disc $\mathbb{D}$ induced by the reproducing kernels of generalized Bergman
spaces. In the first case, we show that all reduced Palm measures $\textit{of
the same order}$ are equivalent. The Radon-Nikodym derivatives are computed
explicitly using regularized multiplicative functionals. We also show that
these determinantal point processes are rigid in the sense of Ghosh and Peres,
hence reduced Palm measures $\textit{of different orders}$ are singular. In the
second case, we show that all reduced Palm measures, $\textit{of all orders}$,
are equivalent. The Radon-Nikodym derivatives are computed using regularized
multiplicative functionals associated with certain Blaschke products. The
quasi-invariance of these determinantal point processes under the group of
diffeomorphisms with compact supports follows as a corollary.
