Quadratic spectral concentration of characteristic functions

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• Kristina Oganesyan (Universitat Autònoma de Barcelona)
• Tuesday 16 July 2024, 12:15-12:35
• Seminar Room 1, Newton Institute.

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DREW01 - Multivariate approximation, discretization, and sampling recovery

A theorem of Donoho and Stark states that decreasing rearrangement increases the quadratic spectral concentration of a square integrable function supported on a sufficiently small set. Importantly, their condition on the smallness of the support turns out to be necessary. In this talk, we restrict ourselves to considering only characeristic functions and, in this setting, we are able to relax the condition of Donoho and Stark. We also discuss various properties of the sets of fixed measure maximizing the quadratic spectral concentration of their characteristic functions. As a corollary, we obtain a sharp (up to a constant) estimate for the L2-norms of non-harmonic trigonometric polynomials with alternating coefficients 1 and -1.

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

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