  One more model of a q-harmonic oscillator based on the q-orthogonal
polynomials of Al-Salam and Carlitz is discussed. The explicit form of
q-creation and q-annihilation operators, q-coherent states and an analog of the
Fourier transformation are established. A connection of the kernel of this
transform with a family of self-dual biorthogonal rational functions is
observed.

Classical Analysis and ODEs;Quantum Algebra