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Half Sampling on Bipartite Graphs

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Abstract

On a bipartite graph G we consider the half sampling problem of uniquely recovering a function from its values on the even vertices, under the appropriate half bandlimited assumption with respect to a Laplacian on the graph. We discuss both finite and infinite graphs, give the appropriate definition of “half bandlimited” that involves splitting the mid frequency, and give an explicit solution to the problem. We discuss in detail the example of a regular tree. We also consider a related sampling problem on graphs that are generated by edge substitution.

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Acknowledgments

Research supported in part by the National Science Foundation, Grant DMS-1162045.

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Authors and Affiliations

  1. Mathematics Department, Cornell University, Malott Hall, Ithaca, NY, 14853, USA

    Robert S. Strichartz

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  1. Robert S. Strichartz
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Correspondence to Robert S. Strichartz.

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Communicated by Hans G. Feichtinger.

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Strichartz, R.S. Half Sampling on Bipartite Graphs. J Fourier Anal Appl 22, 1157–1173 (2016). https://doi.org/10.1007/s00041-015-9452-8

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  • DOI: https://doi.org/10.1007/s00041-015-9452-8

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