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The spectrum of the Leray transform for convex Reinhardt domains in
Authors:David E Barrett  Loredana Lanzani  
Institution:aDepartment of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA;bDepartment of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA
Abstract:The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in View the MathML source. 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.
Keywords:Leray transform  Essential spectrum  Reinhardt domain  Kerzman–  Stein operator  Cauchy integral
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