  Generalizing the case of the usual harmonic oscillator, we look for Bargmann
representations corresponding to deformed harmonic oscillators. Deformed
harmonic oscillator algebras are generated by four operators $a, a^\dagger, N$
and the unity 1 such as $[a,N] = a, [a^\dagger,N] = -a^\dagger$, $a^\dagger a =
\psi(N)$ and $aa^\dagger =\psi(N+1)$. We discuss the conditions of existence of
a scalar product expressed with a true integral on the space spanned by the
eigenstates of $a$ (or $a^\dagger$). We give various examples, in particular we
consider functions $\psi$ that are linear combinations of $q^N$, $q^{-N}$ and
unity and that correspond to q-oscillators with Fock-representations or with
non-Fock-representations.
