Abstract
We extend the symmetric operators of theq-deformed Heisenberg algebra to essentially self-adjoint operators. On the extended domains the product of the operators is not defined. To represent the algebra we had to enlarge the representation and we find a Hilbert space representation of the deformed Heisenberg algebra in terms of essentially self-adjoint operators. The respective diagonalization can be achieved by aq-deformed Fourier transformation.
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