Theorems · Theorem · functional analysis

SchwartzMap.decay

∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
  [inst_3 : NormedSpace ℝ F] (f : SchwartzMap E F) (k n : ℕ),
  ∃ C, 0 < C ∧ ∀ (x : E), ‖x‖ ^ k * ‖iteratedFDeriv ℝ n (⇑f) x‖ ≤ C

All derivatives of a Schwartz function are rapidly decaying.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

3 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace