OAI/Analysis/RieszRectifiability/Kernel/SchwartzSupportLocalization.lean

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Support-preserving Schwartz approximation

Multiplication by expanding cutoffs gives compact approximants whose topological supports remain inside that of the original test. This extends vanishing of tempered distributions on compact tests away from the origin to all Schwartz tests away from the origin, and shows that such distributions depend only on the test's germ there.

  1. theorem OAI.RieszRectifiability.exists_compact_schwartz_approximation_with_support line 22
  2. theorem OAI.RieszRectifiability.tempered_distribution_zero_away_zero_of_compact_tests line 57
  3. theorem OAI.RieszRectifiability.tempered_distribution_eq_of_germ_at_zero line 69