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def definition def or abbrev

extendByZeroLinear

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formal statement (Lean)

 102noncomputable def extendByZeroLinear (N : ℕ) : GalerkinState N →ₗ[ℝ] FourierState2D :=

proof body

Definition body.

 103  { toFun := extendByZero
 104    map_add' := extendByZero_add (N := N)
 105    map_smul' := by
 106      intro c u
 107      -- `simp` expects `c • x`; our lemma is stated in that form.
 108      simpa using (extendByZero_smul (N := N) c u) }
 109
 110/-- `extendByZero` as a *continuous* linear map.
 111
 112This is available because `GalerkinState N` is finite-dimensional, hence every linear map out of it
 113is continuous. -/

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