Integral Averages of Generalization of the Operator -Valued Poisson Kernel and Poisson Kernel Angle Type Formula

Abstract

This study investigates the generalization of the Poisson Kernel and the operator-valued Poisson Kernel from a single variable to two variables, including their integral formulas. The Leibniz rule is utilized to present the average for the extension of the operator-valued Poisson kernel. Furthermore, the angle type formula for the Poisson kernel and its corresponding integral formula, obtained by replacing the single variable with two variables in the original definition, are derived.