Theorems · Theorem · functional analysis

TemperedDistribution.besselPotential_besselPotential_apply

∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
  [inst_2 : InnerProductSpace ℝ E] [inst_3 : FiniteDimensional ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E]
  [inst_6 : NormedSpace ℂ F] (s s' : ℝ) (f : TemperedDistribution E F),
  (TemperedDistribution.besselPotential E F s') ((TemperedDistribution.besselPotential E F s) f) =
    (TemperedDistribution.besselPotential E F (s + s')) f

Defined in: Mathlib.Analysis.Distribution.Sobolev
Cited by: 3 results in Mathlib
Foundations: Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace NormedSpace

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Cited by3

Results whose statement or proof uses this declaration.

TemperedDistribution.memSobolev_besselPotential_iffproof · cited by 3
TemperedDistribution.besselPotential_compL_besselPotentialproof · cited by 0
TemperedDistribution.besselPotential_neg_apply_eq_iffproof · cited by 0