On a piecewise linear enclosure method of continuous functions of many variables

In this paper theorem of an algebraic identity that rewrites a product of n variables as additions of n th power functions is introduced. Theorem of a representation of continuous functions of many variables is provided as an application of theorem of the algebraic identity. Theorem of piecewise linear (PWL) enclosures (having representable lower and upper bounds) of continuous functions is provided as an application of theorem of the representation. Further the examples of PWL enclosures of polynomials are illustrated for imagining the application of these theorems in rigorously analyzing nonlinear systems, e.g., modeling methodology of a piecewise linear differential inclusion describing a nonlinear system dynamics.