English
A new formal multilinear series is obtained by composing each coefficient with a fixed continuous linear map u, i.e., (p.compContinuousLinearMap u) n = (p n).compContinuousLinearMap (fun _ : Fin n => u).
Русский
Получаем новую формальную мультилинейную серию, компонуя каждуюvergoeding коэффициент с фиксированным непрерывным линейным отображением u: (p.compContinuousLinearMap u) n = (p n).compContinuousLinearMap (fun _ : Fin n => u).
LaTeX
$$(p.compContinuousLinearMap u)\; n = (p n).compContinuousLinearMap (\lambda _ : Fin n, u)$$
Lean4
/-- Composing each term `pₙ` in a formal multilinear series with `(u, ..., u)` where `u` is a fixed
continuous linear map, gives a new formal multilinear series `p.compContinuousLinearMap u`. -/
def compContinuousLinearMap (p : FormalMultilinearSeries 𝕜 F G) (u : E →L[𝕜] F) : FormalMultilinearSeries 𝕜 E G :=
fun n => (p n).compContinuousLinearMap fun _ : Fin n => u
