Theorems · Definition · harmonic analysis

SchwartzMap.convolution

{𝕜 : Type u_1} →
  {E : Type u_3} →
    {F₁ : Type u_5} →
      {F₂ : Type u_6} →
        {F₃ : Type u_7} →
          [inst : RCLike 𝕜] →
            [inst_1 : NormedAddCommGroup E] →
              [inst_2 : InnerProductSpace ℝ E] →
                [FiniteDimensional ℝ E] →
                  [inst_4 : MeasurableSpace E] →
                    [BorelSpace E] →
                      [inst_6 : NormedAddCommGroup F₁] →
                        [inst_7 : NormedSpace ℂ F₁] →
                          [inst_8 : NormedSpace 𝕜 F₁] →
                            [inst_9 : SMulCommClass ℂ 𝕜 F₁] →
                              [inst_10 : NormedAddCommGroup F₂] →
                                [inst_11 : NormedSpace ℂ F₂] →
                                  [inst_12 : NormedSpace 𝕜 F₂] →
                                    [inst_13 : SMulCommClass ℂ 𝕜 F₂] →
                                      [inst_14 : NormedAddCommGroup F₃] →
                                        [inst_15 : NormedSpace ℂ F₃] →
                                          [inst_16 : NormedSpace 𝕜 F₃] →
                                            [inst_17 : SMulCommClass ℂ 𝕜 F₃] →
                                              (F₁ →L[𝕜] F₂ →L[𝕜] F₃) →
                                                SchwartzMap E F₁ →ₗ[𝕜] SchwartzMap E F₂ →L[𝕜] SchwartzMap E F₃

The bilinear convolution of Schwartz functions. The continuity in the left argument is provided in SchwartzMap.convolution_continuous_left.

Defined in

Mathlib.Analysis.Fourier.Convolution

Cited by

6 results in Mathlib

Foundations

Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensionalMeasurableSpaceBorelSpaceNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClassNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClassNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClass