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Question: an operator is another term for a function that maps...

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An operator is another term for a function that maps from one function space (e.g., C (R, R), F(R, R), or P2) to another. For instance, see Section 3.5 of the course notes for examples of linear differential operators. The integral operator O : Co (R. R) → Cl (R, R), defined by O(Dx)f(t)dt, Vr ER 0 is an operator mapping a function f to its antiderivative. It takes as its input a function f E CO(R, R) and gives as its output a new function that is in C(R, R). It obtains this new function by integrating f from 0 to x, where x є R. Show that O is a linear operator.

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