Generalized oscillator representations for Calogero Hamiltonians

This paper is a natural continuation of the previous paper J.Phys. A: Math.Theor. 44 (2011) 425204, arXiv 0907.1736 [quant-ph] where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant $\alpha\geq-1/4$ were constructed. Here, we present generalized oscillator representations for all Calogero Hamiltonians with $\alpha\geq-1/4$.These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian.