Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 5 / 5 / a / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 23H / b / Solution Created 2026-09-24 Updated 2026-09-25
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Take the extension from part (a), and choose . The positive function
(1)
belongs to . Positivity extends from nonnegative Schwartz functions to nonnegative elements obtained as limits. Since
(2)
positivity gives
(3)
Taking proves that every positive distribution has order zero.
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