Uniqueness properties of CR-functions

Author:
L. R. Hunt

Journal:
Trans. Amer. Math. Soc. **231** (1977), 329-338

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 Cauchy-Riemann 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 *CR*-function on *M*. The main result of this article is that a *CR*-function is uniquely determined, at least locally, by its values on a real *k*-dimensional 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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1977-0450610-2

Keywords:
Uniqueness,
partial differential equations,
*CR*-functions,
generic manifold

Article copyright:
© Copyright 1977
American Mathematical Society