Theorems · Theorem · functional analysis

Function.HasTemperateGrowth.comp

∀ {D : Type u_4} {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] [inst_4 : NormedAddCommGroup D] [inst_5 : NormedSpace ℝ D]
  {g : E → F} {f : D → E},
  Function.HasTemperateGrowth g → Function.HasTemperateGrowth f → Function.HasTemperateGrowth (g ∘ f)

Composition of two temperate growth functions is of temperate growth.

Defined in

Mathlib.Analysis.Distribution.TemperateGrowth

Cited by

12 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace