Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -IV

TL;DR

This paper extends Erdelyi-Kober fractional integral operators to multivariable cases involving multiple matrix variables, exploring their properties, special cases, and generalized transforms from a statistical perspective.

Contribution

It introduces a multivariable extension of fractional integral operators involving multiple matrix variables, broadening their applicability in statistical and mathematical analysis.

Findings

Extended fractional integral operators to multivariable matrix functions

Identified special cases and generalized matrix transforms

Provided new tools for statistical analysis involving matrix variables

Abstract

In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the arbitrary function is a real-valued scalar function of many $p\times p$ real matrix variables $X_1,...,X_k$. Extension of all standard fractional integral operators to the cases of many matrix variables is considered, along with interesting special cases and generalized matrix transforms.