Duals of Gelfand-Shilov spaces of type $K\{M_p\}$ for the Hankel transformation

For $\mu \ge -\frac{1}{2}$, and under appropriate conditions on the sequence $\{M_p{\}}_{p=0}^{\mathrm{\infty }}$ of weights, the elements, the (weakly, weakly^*, strongly) bounded subsets, and the (weakly, weakly^*, strongly) convergent sequences in the dual of a space ${\mathcal{K}}_{\mu }$ of type Hankel- $K\{M_p\}$ can be represented by distributional derivatives of functions and measures in terms of iterated adjoints of the differential operator $x^{-1}{D}_x$ and the Bessel operator $S_{\mu }=x^{-\mu -\frac{1}{2}}{D}_x{x}^{2\mu +1}{D}_x{x}^{-\mu -\frac{1}{2}}$. In this paper, such representations are compiled, and new ones involving adjoints of suitable iterations of the Zemanian differential operator $N_{\mu }=$ $x^{\mu +\frac{1}{2}}{D}_x{x}^{-\mu -\frac{1}{2}}$ are proved. Prior to this, new descriptions of the topology of the space ${\mathcal{K}}_{\mu }$ are given in terms of the latter iterations.