Mathlib Map

Theorems Β· Definition Β· functional analysis

ContDiffMapSupportedIn.bilinLeftCLM

{π•œ : Type u_1} β†’
  {E : Type u_2} β†’
    [inst : NontriviallyNormedField π•œ] β†’
      [inst_1 : NormedAddCommGroup E] β†’
        [inst_2 : NormedSpace ℝ E] β†’
          {n : β„•βˆž} β†’
            {K : TopologicalSpace.Compacts E} β†’
              {F₁ : Type u_5} β†’
                {Fβ‚‚ : Type u_6} β†’
                  {F₃ : Type u_7} β†’
                    [inst_3 : NormedAlgebra ℝ π•œ] β†’
                      [inst_4 : NormedAddCommGroup F₁] β†’
                        [inst_5 : NormedSpace π•œ F₁] β†’
                          [inst_6 : NormedSpace ℝ F₁] β†’
                            [inst_7 : NormedAddCommGroup Fβ‚‚] β†’
                              [inst_8 : NormedSpace π•œ Fβ‚‚] β†’
                                [inst_9 : NormedSpace ℝ Fβ‚‚] β†’
                                  [inst_10 : NormedAddCommGroup F₃] β†’
                                    [inst_11 : NormedSpace π•œ F₃] β†’
                                      [inst_12 : NormedSpace ℝ F₃] β†’
                                        (F₁ β†’L[π•œ] Fβ‚‚ β†’L[π•œ] F₃) β†’
                                          {g : E β†’ Fβ‚‚} β†’
                                            ContDiff ℝ (↑n) g β†’
                                              ContDiffMapSupportedIn E F₁ n K β†’L[π•œ] ContDiffMapSupportedIn E F₃ n K

The map f ↦ (x ↦ B (f x) (g x)) as a continuous π•œ-linear map on 𝓓^{n}_{K}(E, F₁), where B is a continuous π•œ-linear map and g is a C^n function. TODO: Introduce a type of bundled C^k functions.

Defined in
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn
Cited by
1 results in Mathlib
Foundations
Depth 227 from the axioms Β· uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAlgebraNormedAddCommGroupNormedSpaceNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceNormedAddCommGroupNormedSpaceNormedSpace
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Around this declaration

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ContDiffMapSupportedIn.bilinLeftCLM_apply Β· cited by 0ContDiffMapSupportedIn.bi…DFunLike.coe Β· cited by 62936DFunLike.coeReal Β· cited by 25697RealRingHom.id Β· cited by 18349RingHom.idNormedAddCommGroup Β· cited by 15752NormedAddCommGroupNormedSpace Β· cited by 12499NormedSpaceNontriviallyNormedField Β· cited by 8742NontriviallyNormedFieldSetLike.coe Β· cited by 8199SetLike.coeContinuousLinearMap Β· cited by 5352ContinuousLinearMapENat Β· cited by 4985ENatCompl.compl Β· cited by 2925Compl.complNormedAlgebra Β· cited by 1165NormedAlgebraWithTop.some Β· cited by 1128WithTop.someTopologicalSpace.Compacts Β· cited by 386TopologicalSpace.CompactsContDiff Β· cited by 352ContDiffContDiffMapSupportedIn Β· cited by 107ContDiffMapSupportedInContDiffMapSupportedIn.bilinL…CITED BYCITES

Cites16

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Cited by1

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