A distribution which vanishes on a neighborhood of each point vanishes globally. To prove this, choose a smooth partition of unity subordinate to the neighborhoods. Every test function is a finite sum of its products with the partition members, since its support is compact. The distribution vanishes on each summand. Applying the result to a difference proves that two distributions agreeing locally agree globally. This justifies defining the support of a distribution by removing the union of all open regions on which it is zero.
Target: Periodic primitive with zero mean. Parent: Periodic extension. Intended file: function.bigb. Articles by others on the same topic
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