The Bergman kernel function

In this note, we point out that a large family of n×n matrix valued kernel functions defined on the unit disc $ mathbb{D} subseteq mathbb{C} $ mathbb{D} subseteq mathbb{C} , which were constructed recently in [9], behave like the familiar Bergman kernel function on $ mathbb{D} $ mathbb{D} in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on $ mathbb{D} $ mathbb{D} can be answered using this likeness.