Enhanced Multivariance Product Representation Under an Integral Operator Weight with a Product Type Kernel of Univariate Factors

摘要

This work extends the recently developed method "Enhanced Multivariance Product Representation (EMPR)" to the cases where the weight becomes an integral operator. We assume the kernel boundedness and the symmetry for the integral operator on the focus. We also limit that operator to the cases where its kernel contains just a single additive term which is a product of 2N number of independent variables, where despite N is the true number of the independent variables the integral operator's transformation nature enforces us to use a couple of independent variables for each independent variable, one for the integration and one for the characterization of the outer variable. We show that, even in this quite simple case, the EMPR construction possibility is more than one. Each possibility may produce a different type of EMPR. The work is at conceptual level since the purpose is just formulation. Future works will also contain practicality.