Definition:Functional
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This page is believed by Julius to have a problem that needs the help of a knowledgeable authority, as follows:
Are there functionals that map on other spaces like $\C$? Should I name this as "Real functional" or is there a standard already?
If you are particularly knowledgeable in this area, then you can help ProofWiki by resolving the issues.
Definition
Let $J: S \to \R$ be a mapping:
- $\forall y \in S: \exists x \in \R: J \sqbrk y = x$
Then $J: S \to \R$ is known as a functional, denoted by $J \sqbrk y$.
That is, a functional is a real-valued function whose arguments are themselves mappings.
Are there functionals that map on other spaces like $\C$? Should I name this as "Real functional" or is there a standard already?
If you are particularly knowledgeable in this area, then you can help ProofWiki by resolving the issues.
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Sources
- 1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations ... (next): $\S 1.1$: Functionals. Some Simple Variational Problems
