we shall use a similar approach to obtain quaternionic coherent states.

For the sake of completeness we briefly revisit the procedure for building generalized and nonlinear coherent states.

Let $\{\phi_m\}_{m=0}^{\infty}$ be an orthonormal basis of an abstract separable Hilbert space ${\mathfrak{H}}$. The well known canonical coherent states are defined by: $$\mid z\rangle=e^{-\frac{r^2}{2}}
\sum_{m=0}^{\infty}\frac{z^m}{\sqrt{m!}}\phi_m\in{\mathfrak{H}},
\label{can-comp_CS}$$ where $z = re^{i\theta}\in\mathbb C$, the complex plane.

A possible generalization of the above definition of canonical coherent states, to the so-called nonlinear coherent states, goes as follows: Let ${\mathfrak{D}}$ be an open subset of ${\mathbb{C}}$. For $z\in{\mathfrak{D}}$ set $$\label{can-cs}
\mid z\rangle={\mathcal{N}}(|z|)^{-\frac{1}{2}}
\sum_{m=0}^{\infty}\frac{z^m}{\sqrt{\rho(m)}}\phi_m\in{\mathfrak{H}},$$ where $\{\rho(m)\}_{m=0}^{\infty}$ is a positive sequence of real numbers and ${\mathcal{N}}(|z|)$ is the normalization factor ensuring that $\langle z\mid z\rangle=1.$ If in addition $\{\mid z\rangle \mid z\in
{\mathfrak{D}}\}$ satisfy $$\label{can-res}
\int_{{\mathfrak{D}}}\mid z\rangle\langle z\mid d\mu=I_{{\mathfrak{H}}},$$ where $d\mu$ is an appropriately chosen measure on ${\mathfrak{D}}$ and $I_{{\mathfrak{H}}}$ is the identity operator on ${\mathfrak{H}}$, then $\{\mid z\rangle \mid z\in {\mathfrak{D}}\}$ is said to be a set of nonlinear coherent states on ${\mathfrak{D}}$.\
More generally, (generalized) CS can be constructed as follows: Let $(\Omega,\mu)$ be a measure space and ${\mathbb{H}}$ a closed subspace of $L^2(\Omega,\mu)$. Let $\{\Phi_m\}_{m=0}^{\text{dim}{({\mathbb{H}})}}$, $\text{dim}{({\mathbb{H}})}$ denoting the dimension of ${\mathbb{H}}$, be an orthonormal basis 