Research proof index

The extensional definition of the Kronecker product MatrixMap.kron, in terms of the entries of its image.

The map that takes M and returns M ⊗ₖ C, where C is positive semidefinite, is a completely positive map.

The operational definition of the Kronecker product MatrixMap.kron, that it maps a Kronecker product of inputs to the Kronecker product of outputs. It is the unique bilinear map doing so.

The composition of the dual of the inverse of the dual basis isomorphism with the dual basis isomorphism is the evaluation map.

The composition of the inverse of the dual basis isomorphism with the dual of the dual basis isomorphism is the inverse of the evaluation map.

At every point $x$, the magnitude of the Carleson sum over an antichain of tiles is bounded by a constant depending on $a$ times a maximal function of $f$. The maximal function uses, for each tile $p$, a ball centered at the tile center with radius $8D^{\mathfrak{s}(p)}$.