Theorems · Theorem · functional analysis

TemperedDistribution.fourierMultiplierCLM_smul

∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
  [inst_2 : InnerProductSpace ℝ E] [inst_3 : NormedSpace ℂ F] [inst_4 : FiniteDimensional ℝ E]
  [inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E] {g : E → ℂ},
  Function.HasTemperateGrowth g →
    ∀ (c : ℂ), TemperedDistribution.fourierMultiplierCLM F (c • g) = c • TemperedDistribution.fourierMultiplierCLM F g

Defined in: Mathlib.Analysis.Distribution.FourierMultiplier
Cited by: 0 results in Mathlib
Foundations: Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedAddCommGroup InnerProductSpace NormedSpace FiniteDimensional MeasurableSpace BorelSpace

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