The spectrum of the Leray transform for convex Reinhardt domains in \mathbb C²

2007/10/01 by David E. Barrett, Barrett, David E., Loredana Lanzani +1
Mathematics · #32A26 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CV #msc:32A26

paper · pdf · doi:10.48550/arxiv.0710.0183

To appear in the Journal of Functional Analysis

openalex publication_date 2007/10/01 · arxiv created 2009/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in \mathbb C². Our class is self-dual; it contains some domains with less than C²-smooth boundary and also some domains with smooth boundary and degenerate Levi form. L²-regularity is proved, and essential spectra are computed with respect to a family of boundary measures which includes surface measure. A duality principle is established providing explicit unitary equivalence between operators on domains in our class and operators on the corresponding polar domains. Many of these results are new even for the classical case of smoothly bounded strongly convex Reinhardt domains.

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