Sampling and recovery of multidimensional bandlimited functions via frames |
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Authors: | Benjamin Bailey |
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Institution: | Department of Mathematics, Texas A&M University, College Station, TX 77843, USA |
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Abstract: | In this paper, we investigate frames for L2d−π,π] consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for bandlimited functions with a fairly general frequency domain. The stability of said formula under various perturbations in the sampled data is investigated, and a computationally manageable simplification of the main oversampling theorem is given. Also, a generalization of Kadec's 1/4 theorem to higher dimensions is considered. Finally, the developed techniques are used to approximate biorthogonal functions of particular exponential Riesz bases for L2−π,π], and a well-known theorem of Levinson is recovered as a corollary. |
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Keywords: | Frames Sampling Kadec Levinson Riesz basis Oversampling |
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