Theorems · Definition · functional analysis

RKHS.kernel

{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] →
                  [RKHS 𝕜 H X V] → [CompleteSpace H] → [CompleteSpace V] → Matrix X X (V →L[𝕜] V)

The kernel of a reproducing kernel Hilbert space is a matrix of entries given by the kernel functions.

Defined in

Mathlib.Analysis.InnerProductSpace.Reproducing

Cited by

12 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceRKHSCompleteSpaceCompleteSpace