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Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. (English) Zbl 1458.94192

Summary: In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values \(\{\langle f, \psi_a(\cdot- x_j,\cdot- y_k)\rangle:j,k\in\mathbb{J}\}\) generated by single averaging function and average sampled values \(\{\langle f, \psi_{x_j , y_k}\rangle:j,k\in\mathbb{J}\}\) generated by multiple averaging functions. Two fast reconstruction algorithms for these two types of average sampled values are provided.

MSC:

94A20 Sampling theory in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C15 General harmonic expansions, frames
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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