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Construct a linear functional on L2([0, 1], dA) such that X(f) = ||f||2, for a function fe L2([0, 1], dA). What is the kernel

Construct a linear functional on L2([0, 1], dA) such that X(f) = ||f||2, for a function fe L2([0, 1], dA). 

Construct a linear functional on L2([0, 1], dA) such that X(f) = ||f||2, for a function fe L2([0, 1], dA). What is the kernel function of the Riesz integral of X? representation

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