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Average sampling in mixed shift-invariant subspaces with generators in hybrid-norm spaces
  • Haizhen Li,
  • Yan Tang,
  • Yingchun Jiang
Haizhen Li
guilin institute of information technology

Corresponding Author:[email protected]

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Yan Tang
Guilin University of Electronic Technology
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Yingchun Jiang
Guilin University of Electronic Technology


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.
14 Jun 2022Published in Far East Journal of Applied Mathematics volume 113 on pages 45-66. 10.17654/0972096022010