Reconstruction of functions in principal shift-invariant subspaces of mixed Lebesgue spaces

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In this paper, we discuss to the nonuniform sampling problem in principal shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast reconstruction algorithm which allows to exactly reconstruct the functions in the principal shift-invariant subspaces as long as the sampling set X={(xⱼ,yₖ):k,j∈ J} is sufficiently dense. Our results improve the result in LiLiu.