Uniqueness properties of CRfunctions
Author:
L. R. Hunt
Journal:
Trans. Amer. Math. Soc. 231 (1977), 329338
MSC:
Primary 32D15; Secondary 32C05
MathSciNet review:
0450610
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Abstract: Let M be a real infinitely differentiable closed hypersurface in X, a complex manifold of complex dimension . The uniqueness properties of solutions to the system , where is the induced CauchyRiemann operator on M, are of interest in the fields of several complex variables and partial differential equations. Since dM is linear, the study of the solution to the equation is sufficient for uniqueness. A solution to this homogeneous equation is called a CRfunction on M. The main result of this article is that a CRfunction is uniquely determined, at least locally, by its values on a real kdimensional generic submanifold of M with . The facts that is generic and together form the lower dimensional analogue of the concept of noncharacteristic.
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 M. J. Strauss and F. Trèves, Firstorder linear PDEs and uniqueness in the Cauchy problem, J. Differential Equations 15 (1974), 195209. MR 48 #9076. MR 0330739 (48:9076)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197704506102
PII:
S 00029947(1977)04506102
Keywords:
Uniqueness,
partial differential equations,
CRfunctions,
generic manifold
Article copyright:
© Copyright 1977
American Mathematical Society
