Theorems · Theorem · functional analysis
TemperedDistribution.MemSobolev.lineDerivOp
∀ {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 : InnerProductSpace ℂ F] [inst_7 : CompleteSpace F] {s : ℝ} {f : TemperedDistribution E F},
TemperedDistribution.MemSobolev s 2 f →
∀ {m : E}, TemperedDistribution.MemSobolev (s - 1) 2 (LineDeriv.lineDerivOp m f)The directional derivative maps H ^ s to H ^ {s - 1}.
- Defined in
- Mathlib.Analysis.Distribution.Sobolev
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- CompleteSpacestatement and proof · cited by 2,532
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
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