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A Constrained Optimization Problem for the Fourier Transform: Quantitative Analysis

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Abstract

Among functions f majorized by indicator functions \(1_E\), which functions have maximal ratio \(\Vert {\widehat{f}}\Vert _q/|E|^{1/p}\)? We establish a quantitative answer to this question for exponents q sufficiently close to even integers, building on previous work proving the existence of such maximizers.

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  1. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    Dominique Maldague

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  1. Dominique Maldague
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Correspondence to Dominique Maldague.

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Maldague, D. A Constrained Optimization Problem for the Fourier Transform: Quantitative Analysis. J Geom Anal 29, 1259–1301 (2019). https://doi.org/10.1007/s12220-018-0038-y

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  • DOI: https://doi.org/10.1007/s12220-018-0038-y

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