Memoires de la Societe Mathematique de France
Volume: 123; 2011; 136 pp; Softcover
MSC: Primary 32; 58;
Print ISBN: 978-2-85629-304-1
Product Code: SMFMEM/123
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Individual Member Price: $33.60
Projections in Several Complex VariablesShare this page
A publication of the Société Mathématique de France
This work consists two parts. In the first part, the author studies completely the heat equation method of Menikoff-Sjöstrand and applies it to the Kohn Laplacian defined on a compact orientable connected CR manifold. He then gets the full asymptotic expansion of the Szegő projection for \((0, q)\) forms when the Levi form is non-degenerate. This generalizes a result of Boutet de Monvel and Sjöstrand for \((0,0)\) forms. The author's main tools are Fourier integral operators with complex valued phase Melin and Sjöstrand functions.
In the second part, the author obtains the full asymptotic expansion of the Bergman projection for \((0, q)\) forms when the Levi form is non-degenerate. This also generalizes a result of Boutet de Monvel and Sjöstrand for \((0,0)\) forms. He introduces a new operator analogous to the Kohn Laplacian defined on the boundary of a domain and applies the heat equation method of Menikoff and Sjöstrand to this operator. He obtains a description of a new Szegő projection up to smoothing operators and gets his main result by using the Poisson operator.
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Table of Contents
Table of Contents
Projections in Several Complex Variables
Graduate students and research mathematicians interested in analysis.