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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Ideals of holomorphic functions with $ C\sp \infty$ boundary values on a pseudoconvex domain


Authors: Edward Bierstone and Pierre D. Milman
Journal: Trans. Amer. Math. Soc. 304 (1987), 323-342
MSC: Primary 32F15; Secondary 32E25, 35N15, 46J15
MathSciNet review: 906818
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Abstract: We give natural sufficient conditions for the solution of several problems concerning division in the space $ {\mathcal{A}^\infty }(\Omega )$ of holomorphic functions with $ {\mathcal{C}^\infty }$ boundary values on a pseudoconvex domain $ \Omega $ with smooth boundary. The sufficient conditions come from upper semicontinuity with respect to the analytic Zariski topology of a local invariant of coherent analytic sheaves (the "invariant diagram of initial exponents"), and apply to division in the space of $ {\mathcal{C}^\infty }$ Whitney functions on an arbitrary closed set. Our theorem on division in $ {\mathcal{A}^\infty }(\Omega )$ follows using Kohn's theorem on global regularity in the $ \bar \partial $-Neumann problem.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0906818-9
Article copyright: © Copyright 1987 American Mathematical Society