On the Local Regularity of the Hilbert Transform

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Yifei Pan , Jianfei Wang , Yu Yan This is my paper · ORCID

classification math.CAmath.CV

keywords localhilbertregularitytransformanalyticityconsideredobtainedreal

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In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained.

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A variational argument yields an asymptotically power-optimal covariance shrinker for high-dimensional Hotelling's T-squared tests under general covariance spectra.