Theorems · Theorem · functional analysis

Function.HasTemperateGrowth.fun_smul

∀ {𝕜 : Type u_2} {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 : NontriviallyNormedField 𝕜]
  [inst_5 : NormedAlgebra ℝ 𝕜] [inst_6 : NormedSpace 𝕜 F] {f : E → 𝕜} {g : E → F},
  Function.HasTemperateGrowth f → Function.HasTemperateGrowth g → Function.HasTemperateGrowth fun i => f i • g i

Eta-expanded form of Function.HasTemperateGrowth.smul The product of two functions of temperate growth is again of temperate growth. Version for scalar multiplication.

Defined in

Mathlib.Analysis.Distribution.TemperateGrowth

Cited by

0 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpace