Arik, M.; Coon, D. D. Hilbert spaces of analytic functions and generalized coherent states. (English) Zbl 0941.81549 J. Math. Phys. 17, No. 4, 524-526 (1976). Generalized creation and annihilation operators are introduced, which in a certain limit \((q\rightarrow 1)\) become the usual boson creation and annihilation operators. These operators are bounded. From them generalized coherent states are constructed, which form an overcomplete basis in a Hilbert space \(H_q\) of analytic functions, and in the limit \(q\rightarrow 1\) become the usual coherent states of quantum optics. The scalar product in \(H_q\) is written in such a way that a “basic integration” is involved in its expression. It is shown that \(H_q\) reduces in the limit \(q\rightarrow 1\) to the Bargmann-Segal Hilbert space of entire functions and in the limit \(q\rightarrow 0\) to the Hardy-Lebesgue space. Reviewer: E.Kyriakopoulos (MR 58:14603) Cited in 5 ReviewsCited in 164 Documents MSC: 81R30 Coherent states 46E20 Hilbert spaces of continuous, differentiable or analytic functions Keywords:generalized coherent states; Hilbert space of analytic functions; Bargmann-Segal Hilbert sapce of entire functions; Hardy-Lebesgue space PDFBibTeX XMLCite \textit{M. Arik} and \textit{D. D. Coon}, J. Math. Phys. 17, 524--526 (1976; Zbl 0941.81549) Full Text: DOI