Theorems · Theorem · functional analysis

RKHS.adjoint_kerFun

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {X : Type u_2} {V : Type u_3} [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] {H : Type u_4} [inst_3 : NormedAddCommGroup H] [inst_4 : InnerProductSpace 𝕜 H]
  [inst_5 : RKHS 𝕜 H X V] [inst_6 : CompleteSpace H] [inst_7 : CompleteSpace V] (x : X) (f : H),
  (ContinuousLinearMap.adjoint (RKHS.kerFun H x)) f = f x

Point evaluation f ↦ f x is the adjoint of the kernel function kerFun H x.

Defined in

Mathlib.Analysis.InnerProductSpace.Reproducing

Cited by

2 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceRKHSCompleteSpaceCompleteSpace