Functionals->functions of infinite variables?

  1. 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.
     
  2. jcsd
  3. mathman

    mathman 6,479
    Science Advisor
    Gold Member

    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.
     
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