(see also references therein). In these papers it has been shown that the functions, $e^{-|z|^2/2}H_{n,m}(z,\overline{z})$ are eigensolutions of the Landau problem [@AFG; @Ghan]. Recently, several interesting features of the $H_{n,m}(z,\overline{z})$ have been studied by fixing either $n=0$ or $m=0$. In fact, by so fixing one can recover the holomorphic and anti-holomorphic subspaces of a certain $L^2$-space and the subspaces so obtained can also be identified as the well known Bargmann spaces of holomorphic and anti-holomorphic functions. These are also reproducing kernel Hilbert spaces with reproducing kernels associated to the canonical coherent states. More generally, other reproducing kernel Hilbert spaces have been obtained using subsets of $H_{n,m}(z,\overline{z})$ as bases [@AFG; @Nic], which also admit coherent states. In [@Nic], these coherent states have been used to implement quantizations of $\mathbb C$. In [@Nic; @Ga] the Hermite polynomials $H_{n,m}(z,\overline{z})$ and $H_n(z)$ and kernels associated with these polynomials have been used to obtain coherent states and the authors have used the CS so obtained to study some quantum phenomena and quantizations. In fact, the procedure used in [@Nic; @Ga] to build CS was earlier worked out in [@Iwa] and later in [@Ali; @Thi3] as generalization of the definition of canonical CS. In this paper 