Abstract
Deformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint a and a†, and two self-adjoint N and the unity 1 such as: [Formula: see text] The Bargmann Hilbert space is defined as a space of functions, holomorphic in a ring of the complex plane, equipped with a scalar product involving a true integral. In a Bargmann representation, the operators of a Deformed Harmonic Oscillator Algebra act on a Bargmann Hilbert space and the creation (or the annihilation operator) is the multiplication by z. We discuss the conditions of existence of Deformed Harmonic Oscillator Algebras assumed to admit a given Bargmann representation.
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