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On the Nonpropagation of Zero Sets of Solutions of Certain Homogeneous Linear Partial Differential Equations across Noncharacteristic Hyperplanes.
Interim technical rept.,
SCHOOL OF AEROSPACE MEDICINE BROOKS AFB TX
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In this paper nonuniqueness has been obtained for spaces smaller than the space of infinitely differentiable functions, which is an improvement of Cohens nonuniqueness result. In the course of developing these results we made a study of some of the many function spaces lying between the space of infinitely differentiable functions and the space of real analytic functions. These are generalizations of the spaces studied by Gevrey, Friedman, and Hormander. Because the very definition of these spaces depends on the growth of derivatives, we include for completeness a proof of the formula for the nth derivative of the composition of two functions.
APPROVED FOR PUBLIC RELEASE