Average sampling in mixed shift-invariant subspaces with generators in hybrid-norm spaces
• Haizhen Li,
• Yan Tang
Haizhen Li
Guilin University of Electronic Technology
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Yan Tang
Guilin University of Electronic Technology
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## Abstract

This paper mainly studies the average sampling and reconstruction in shift-invariant subspaces of mixed Lebesgue spaces $L^{p,q}(\mathbb{R}^{d+1})$, under the condition that the generator $\varphi$ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form, which is weaker than the usual assumption of Wiener amalgam space and allows to control the orders $p,q$. First, the sampling stability for two kinds of average sampling functionals are established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-varying shift-invariant signals from the average samples.

#### Peer review status:UNDER REVIEW

13 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
15 Apr 2021Assigned to Editor
15 Apr 2021Submission Checks Completed
26 Apr 2021Reviewer(s) Assigned