Nonuniform Sampling Theorem for Non-decaying Signals in Mixed-Norm Spaces \(L_{\vec{p},\frac{1}{\omega }}(\mathbb{R}^{d})\)

In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of $L_{\overrightarrow{p},\frac{1}{\omega }}({\mathbb{R}}^d)$ $L_{\vec{p},\frac{1}{\omega }}(\mathbb{R}^{d})$ . Firstly, we will give a stability theorem for the shift-invariant subspace $V_{\overrightarrow{p},\frac{1}{\omega }}(\phi )$ $V_{\vec{p},\frac{1}{\omega }}(\varphi )$ . Secondly, an ideal sampling in $W_{\overrightarrow{p},\frac{1}{\omega }}^s({\mathbb{R}}^d)$ $W_{\vec{p},\frac{1}{\omega }}^{s}(\mathbb{R}^{d})$ is proved, and thirdly, a convergence theorem (or algorithm) is shown for $V_{\overrightarrow{p},\frac{1}{\omega }}(\phi )$ $V_{\vec{p},\frac{1}{\omega }}(\varphi )$ . It should be pointed out that the auxiliary function $\phi$ $\varphi $ enjoys the membership in a Wiener amalgam space.