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Linear Functionals, Continuous Derivatives and Scalars

Note that in problem 2, <x,l_1> = l_1(x), etc

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the differentiation and integration operators are linear

the squaring operation is not linear, and neither is the integral of the square of f(t)

// take int_a^b to mean the integral from a to b //

then int_0^1 t^2 f(t) is a linear functional, since f is unaffected

int_1^2 f(t^2) dt = int_1^4 f(u) du which is ...

Solution Summary

Linear Functionals, Continuous Derivatives, Vector Spaces and Scalars are investigated.