The structure of certain types of quasi shift-invariant spaces, which takethe form$V(\psi,\mathcal{X}):=\overline{\text{span}}^{L_2}\{\psi(\cdot-x_j):j\in\mathbb{Z}\}$for a discrete set $\mathcal{X}=(x_j)\subset\mathbb{R}$ is investigated.Additionally, the relation is explored between pairs $(\psi,\mathcal{X})$ and$(\phi,\mathcal{Y})$ such that interpolation of functions in$V(\psi,\mathcal{X})$ via interpolants in $V(\phi,\mathcal{Y})$ solely from thesamples of the original function is possible and stable. Some conditions aregiven for which the sampling problem is stable, and for which recovery offunctions from their interpolants from a family of spaces$V(\phi_\alpha,\mathcal{Y})$ is possible.
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