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

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Abstract

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

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Acknowledgements

The authors would like to thank the referees for carefully reading the manuscript, giving valuable comments and suggestions to improve the results.

Funding

This project is partially supported by the Natural Science Foundation of Tianjin City, China (Grant No. 18JCYBJC16300).

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  1. School of Mathematical Sciences, TianGong University, Tianjin, 300387, People’s Republic of China

    Junjian Zhao

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Zhao, J. Nonuniform Sampling Theorem for Non-decaying Signals in Mixed-Norm Spaces \(L_{\vec{p},\frac{1}{\omega }}(\mathbb{R}^{d})\). Acta Appl Math 189, 2 (2024). https://doi.org/10.1007/s10440-023-00631-0

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