Unique continuation theorems for the\bar \partial - Operator and applications |
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Authors: | Steven Bell |
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Institution: | 1. Mathematics Department, Purdue University, 47907, West Lafayette, IN, USA
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Abstract: | We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz
0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported
away fromz
0 cannot vanish to infinite order atz
0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the
problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in
several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection
and kernel in planar domains.
Research supported by NSF Grant DMS-8922810. |
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Keywords: | Math Subject Classification" target="_blank">Math Subject Classification 35N15 32H10 |
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