Global Real Analyticity of the Kohn–Laplacian on Pseudoconvex CR Manifolds with Comparable Levi Form

In this paper, we study the global analytic hypoellipticity of the □ b operator on a general CR manifold of real dimension ( 2 n - 1 ) , with n ≥ 3 . In particular, if M is a compact, real analytic, pseudoconvex CR manifold satisfying the D ϵ ( q ) and ( C R - P q ) conditions, and a special propert...

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Bibliographic Details
Published in:Complex analysis and operator theory 2017-08, Vol.11 (6), p.1329-1350
Main Author: Ha, Ly Kim
Format: Article
Language:English
Subjects:
Analysis
Differential equations
Manifolds (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial differential equations
Thermal analysis
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Summary:In this paper, we study the global analytic hypoellipticity of the □ b operator on a general CR manifold of real dimension ( 2 n - 1 ) , with n ≥ 3 . In particular, if M is a compact, real analytic, pseudoconvex CR manifold satisfying the D ϵ ( q ) and ( C R - P q ) conditions, and a special property for vector field T , we consider the following nonelliptic partial differential equation □ b u = f . If f is globally real analytic, we conclude that u is globally real analytic as well. The methods applied in this work are inspired from Tartakoff (1(4):283–311, 1976 ) and Tartakoff (89–90:85–116 1981 ).
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-016-0570-3