  The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples.
The first one involves deformed complex Hermite polynomials built using
finite-dimensional irreducible representations of the group ${\rm
GL}(2,{\mathbb C})$ of invertible $2 \times 2$ matrices with complex entries.
It reveals interesting aspects of these representations. The second example is
based on a pseudo-bosonic generalization of operator-valued functions of a
complex variable which resolves the identity. We show that such a
generalization allows one to obtain a quantum pseudo-bosonic version of the
complex plane viewed as the canonical phase space and to understand functions
of the pseudo-bosonic operators as the quantized versions of functions of a
complex variable.
