The Leray transform: distinguished measures, symmetries and polygamma inequalities

2024/01/30 by Edholm, Luke D., Shelah, Yonatan
#26D15 #32A26 #33B15 #47A30 #65B15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.17490

Abstract

New symmetries, norm computations and spectral information are obtained for the Leray transform on a class of unbounded hypersurfaces in ℂ². Emphasis is placed on certain distinguished measures, with results on operator norm monotonicity established by proving new polygamma inequalities. Classical techniques of Bernstein-Widder and Euler-Maclaurin play crucial roles in our analysis. Underpinning this work is a projective geometric theory of duality, which manifests here in the form of Hölder invariance.

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