When I was reading the Sub-Bergman Hilbert spaces (doi:10.1016/j.jmaa.2005.12.035), written by Saida Sultanic, I noticed that in page 641, he mentioned:
Before we continue our analysis of these spaces, we will recall the definition of rescaling kernels. Let $k$ and $j$ be kernel functions for Hilbert function spaces $\mathcal{H}_k$ and $\mathcal{H}_j$, respectively. We say that $j$ is obtained from $k$ by rescaling or renormalizing if there is a nowhere vanishing function $δ$ so that $$ j(ζ,λ) = \overline{δ(ζ)}δ(λ)k(ζ,λ). $$
But I have checked all the books I could find related with reproducing kernel, only to find nothing about rescaling kernel index.
I wonder what it is exactly. Does rescaling kernel have other more formal names that I can find on the book?