The eigenvalue estimation of spatio-spectral limiting operators

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• Azita Mayeli (City University of New York)
• Tuesday 16 July 2024, 14:00-14:40
• Seminar Room 1, Newton Institute.

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DREW01 - Multivariate approximation, discretization, and sampling recovery

Let F, S be bounded measurable sets in Rd. Let PF : L2 (Rd) → L2 (Rd) be the orthogonal projection on the subspace of functions with compact support on F, and let BS : L2 (Rd) → L2 (Rd) be the orthogonal projectionon the subspace of functions with Fourier transforms having compact support on S. We define the spatio-spectral limiting operator as a composition of the orthogonal projections BSPF BS : L2 (Rd) → L2 (Rd). The non-asymptotic eigenvalue distribution of this operator in dimension d = 1 has been studied for the case when F and S are both intervals. In higher dimensions, some asymptotic results are known when S and F are balls, and these results have proved useful for various applications, such as interpolation. In this talk, I will report on the non-asymptotic distributional estimates of the eigenvalue sequence of this operator for d ≥ 1 for more general spatio and frequency domains F and S, resepectively. The significance of these estimates lies in their diverse applications in wireless communications, medical imaging,signal processing, geophysics, and astronomy. This is a joint work with Kevin Hughes of Edinburgh Napier University and Arie Israel of The University of Texas at Austin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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