Theorems · Definition · functional analysis

SchwartzMap.derivCLM

(𝕜 : Type u_2) →
  (F : Type u_8) →
    [inst : NormedAddCommGroup F] →
      [inst_1 : NormedSpace ℝ F] →
        [inst_2 : RCLike 𝕜] → [inst_3 : NormedSpace 𝕜 F] → SchwartzMap ℝ F →L[𝕜] SchwartzMap ℝ F

The 1-dimensional derivative on Schwartz space as a continuous 𝕜-linear map.

Defined in: Mathlib.Analysis.Distribution.SchwartzSpace.Deriv
Cited by: 5 results in Mathlib
Foundations: Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace RCLike NormedSpace

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Around this declaration

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

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
RingHom.idstatement · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
ContinuousLinearMapstatement · cited by 5,352
RCLikestatement and proof · cited by 2,829
derivproof · cited by 676
SchwartzMapstatement and proof · cited by 251
SchwartzMap.mkCLMproof · cited by 0

Cited by6

Results whose statement or proof uses this declaration.

SchwartzMap.integral_bilinear_deriv_right_eq_neg_leftproof · cited by 3
TemperedDistribution.derivCLMproof · cited by 2
SchwartzMap.tsupport_derivCLM_subsetstatement · cited by 0
TemperedDistribution.derivCLM_apply_applystatement · cited by 0
TemperedDistribution.derivCLM_toTemperedDistributionCLM_eqstatement and proof · cited by 0
SchwartzMap.derivCLM_applystatement · cited by 0