Yes functional analysis is the study of functionals (up to some extend). Why we are so curious to study functionals? Some applications please for the motivations to me.
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Quantum mechanics is a big one – operatorerror Nov 24 '16 at 18:04
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1Functional analysis is less "the study of functionals" and more "linear algebra in infinite dimensional spaces". In that context, functionals (that is, dual spaces) are the closest analog we have to dot-products outside of Hilbert Spaces – Ben Grossmann Nov 24 '16 at 18:06
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@Kaynex that notion of a functional doesn't traditionally fall under the field of "functional analysis". – Ben Grossmann Nov 24 '16 at 18:08