Is there any linear map  that lowers the number of variables of functions, namely a map that  maps a function of several variables to functions of one variable and at the same time the original function can be reconstructed with its image through an explicit form.  
 For example, $$T: C(\mathbb{R}^n)\rightarrow C(\mathbb{R})$$
                  $$f(\mathbb {x})\rightarrow F(t)$$
such that
   $$f(\mathbb {x})=\int_{\mathbb{R}}K(\mathbf{x},t)F(t)dt,\quad \forall f\in C(\mathbb{R}^n)$$
with some kernel $K$?  
It has not to be this specific form. My key problem is to find transforms that lowers the number of variables of functions and store $f(x)$ separately  in $F(t)$, which preserves the information, and   $K(\mathbf{x},t)$, which keeps its "location".