On completeness of coherent states in noncommutative spaces with the generalised uncertainty principle

Abstract

Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the generalised uncertainty relation by finding the resolution of unity with a positive definite weight function. The weight function, which is sometimes known as the Borel measure, is obtained through explicit analytic solutions of the Stieltjes and Hausdorff moment problem with the help of the standard techniques of the inverse Mellin transform.