Factorizations of Kernels and Reproducing Kernel Hilbert Spaces

TL;DR

This paper explores the structure of reproducing kernel Hilbert spaces, focusing on kernel factorizations, triviality of isometric multipliers, dilation conditions, and classification of Brehmer submodules.

Contribution

It provides new results on kernel factorizations, conditions for dilations, and classifications of submodules in reproducing kernel Hilbert spaces.

Findings

Isometric multipliers are trivial for a large class of spaces.

Conditions for obtaining specific dilations are established.

Classification of Brehmer type submodules is provided.

Abstract

The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also gives for certain spaces conditions for obtaining a particular type of dilation, as well as a classification of Brehmer type submodules.