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.

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".