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Sampling and Reconstruction of Concentrated Reproducing Kernel Signals in Mixed Lebesgue Spaces

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Abstract

In this paper, we mainly study the deterministic or random sampling and reconstruction of concentrated signals in the reproducing kernel subspaces of mixed Lebesgue spaces \(L^{p,q}({\mathbb {R}}\times X)\), where X is a metric space with non-negative Borel measure. We first revisit and reformulate the iterative reconstruction algorithms in reproducing kernel subspaces of mixed Lebesgue spaces. Then, we establish a weighted sampling stability inequality and propose an algorithm to provide a good approximation to the concentrated signals in the reproducing kernel subspaces. Finally, we prove that the concentrated signals can also be approximately reconstructed from the random samples with high probability.

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Acknowledgements

The project is partially supported by the National Natural Science Foundation of China (No. 12261025), the Guangxi Natural Science Foundation (No. 2019GXNSFFA245012), Center for Applied Mathematics of Guangxi (No. AD23023002), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Yingchun Jiang & Yajing Zhang

  2. Center for Applied Mathematics of Guangxi(GUET), Guilin, 541004, People’s Republic of China

    Yingchun Jiang & Yajing Zhang

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  1. Yingchun Jiang
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  2. Yajing Zhang
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Correspondence to Yajing Zhang.

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Communicated by See Keong Lee.

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Jiang, Y., Zhang, Y. Sampling and Reconstruction of Concentrated Reproducing Kernel Signals in Mixed Lebesgue Spaces. Bull. Malays. Math. Sci. Soc. 47, 16 (2024). https://doi.org/10.1007/s40840-023-01616-w

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  • DOI: https://doi.org/10.1007/s40840-023-01616-w

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