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I have been reading up on Green Functions and I stumbled upon the term "linear functional". I know the properties of the linear operator, but i can't really grasp what a functional does.

In my notes it says that it indicates a linear function whose domain is a function space, and that is maps a function to its value at a point, such that:

[tex]L_ξ=u(ξ)[/tex]

Can someone clarify what this means? I don't understand the qualitative aspect, i.e. what it actually "does". Is it just a way to talk about the operation of going from the function domain space to its value space? What is the added value of using it instead of saying X->Y?

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# What is a (linear) functional?

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