Theorems · Definition · functional analysis

ContinuousLinearMap.fpowerSeries

{𝕜 : Type u} →
  {E : Type v} →
    {F : Type w} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] → (E →L[𝕜] F) → E → FormalMultilinearSeries 𝕜 E F

Formal power series of a continuous linear map f : E →L[𝕜] F at x : E: f y = f x + f (y - x).

Defined in

Mathlib.Analysis.Calculus.FormalMultilinearSeries

Cited by

7 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace