Representations of the Gegenbauer Oscillator Algebra and the Overcompleteness of Sequences of Nonlinear Coherent States
نویسنده
چکیده
The main purpose of this paper is to investigate a generalized oscillator algebra, naturally associated to the Gegenbauer polynomials and a related class of nonlinear coherent vectors. We derive their overcompleteness relation, in so doing, the partition of unity in terms of the eigenstates of the sequences of coherent vectors is established. It turns out that, in making up such relation, the positivity of the obtained measure is intimately connected, up to a conjecture, to the parameter appearing in the beta distribution. An example of complex hypercontractivity property for an “ultraspherical” Hamiltonian is developed to illustrate our theory.
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