Functionals->functions of infinite variables?

[HomogenousCow]

If we think of a functional as a function of the infinite number of taylor coefficients of the variable function, aren't they then just normal functions, a map between a set of reals to another set of reals.

 

[mathman]

If we think of a functional as a function of the infinite number of taylor coefficients of the variable function, aren't they then just normal functions, a map between a set of reals to another set of reals.

The "variable function" may not have a Taylor expansion, or if it does for part of its domain, the expansion may not hold for the rest. Simple example, L2 includes discontinuous functions, functions without derivatives, etc.