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Functionals->functions of infinite variables?

by HomogenousCow
Tags: infinite, variables
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HomogenousCow
#1
May25-13, 12:31 PM
P: 366
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.
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mathman
#2
May25-13, 03:55 PM
Sci Advisor
P: 6,109
Quote Quote by HomogenousCow View Post
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.


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