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An Application of Logic to Analysis

Published online by Cambridge University Press:  20 November 2018

Joseph Becker  and
Leonard Lipshitz
Joseph Becker
Affiliation:
Purdue University, Lafayette, Indiana
Leonard Lipshitz
Affiliation:
Purdue University, Lafayette, Indiana
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Let F be a complex analytic subvariety of an open subset of Cn and p ϵ V let be the germs at p of holomorphic, weakly holomorphic, infinitely differentiable, and k times continuously differentiate functions respectively. Spallek [15] has shown that for any p £ V there exists an integer such that , generalizing the result of Malgrange [12] that .In [14], Siu proved Spallek's result from a more sheaf theoretic point of view and showed the minimal integer function is bounded on compact sets. Bloom [7] reproved Malgrange's result by using differential operators on varieties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 83 - 91
Copyright
Copyright © Canadian Mathematical Society 1976

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