  This work addresses a construction of a dual pair of nonlinear coherent
states (NCS) in the context of changes of bases in the underlying Hilbert space
for a model pertaining to the condensed matter physics, which obeys a
$f$-deformed Heisenberg algebra. The existence and properties of reproducing
kernel in the NCS Hilbert space are studied and discussed; the probability
density and its dynamics in the basis of constructed coherent states are
provided. A Glauber-Sudarshan $P$-representation of the density matrix and
relevant issues related to the reproducing kernel properties are presented.
Moreover, a NCS quantization of classical phase space observables is performed
and illustrated in a concrete example of $q$-deformed coherent states. Finally,
an exposition of quantum optical properties is given.
