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Theorems · Theorem · functional analysis

Function.HasTemperateGrowth.fun_mul

∀ {R : Type u_3} {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedRing R]
  [inst_3 : NormedAlgebra ℝ R] {f g : E → R},
  Function.HasTemperateGrowth f → Function.HasTemperateGrowth g → Function.HasTemperateGrowth fun i => f i * g i

Eta-expanded form of Function.HasTemperateGrowth.mul The product of two functions of temperate growth is again of temperate growth.

Defined in
Mathlib.Analysis.Distribution.TemperateGrowth
Cited by
2 results in Mathlib
Foundations
Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceNormedRingNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TemperedDistribution.MemSobolev.laplacian · cited by 0MemSobolev.laplacianTemperedDistribution.MemSobolev.lineDerivOp · cited by 0MemSobolev.lineDerivOpReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNormedAlgebra · cited by 1165NormedAlgebraNormedRing · cited by 924NormedRingFunction.HasTemperateGrowth · cited by 88Function.HasTemperateGrow…Function.HasTemperateGrowth.mul · cited by 3HasTemperateGrowth.mulHasTemperateGrowth.fun_mulCITED BYCITES

Cites7

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Cited by2

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