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If a functional is a mapping from a function space into real numbers, then can something as simple as $J[f]=f(a)+2$, where $f$ is a function and $a$ is a real number, be regarded as a functional?

Gerry Myerson
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apadana
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Yes, say your function space $X$ is such that $a \in \operatorname{Dom}(f)$ for all $f \in X$, then the map $J : f \mapsto f(a) + 2$ is a functional.

Of course, if $a \notin \operatorname{Dom}(f)$ for some $f \in X$, then $J$ would be ill-defined.

Olivier Roche
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