instContinuousMapClass — Mathlib

English

If g has compact support, then the right convolution f ⋆ g is ContDiff of order n whenever f is Locally Integrable and g is ContDiffOn.

Русский

Если у g компактная опора, то правая свёртка f ⋆ g гладкая степени n при условии локальной интегрируемости f и contDiffOn(g).

LaTeX

$$$$\\text{contDiff}_{ℝ}^n (f⋆ g) \\text{ when } f\\in L^1_{loc}, g\\in C^n_c.$$$$

Lean4

instance (B : Type*) (E F : outParam <| Type*) [NormedAddCommGroup E] [NormedAddCommGroup F] [NormedSpace ℝ E]
    [NormedSpace ℝ F] (n : outParam ℕ∞) (K : outParam <| Compacts E) [ContDiffMapSupportedInClass B E F n K] :
    ContinuousMapClass B E F where map_continuous f := (map_contDiff f).continuous

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