Functional analysis is the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces, as well as measure, ...

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Gateaux variation (Functional Derivative) of functional with convolution

Given the following functional $F[f]=\int f(x) \log(g(x)) dx$ find Gateaux variation. Also, $g(x)$ is given by convolution $g(x)=y(x) * f(x)=\int y(\tau) f(x-\tau) d\tau$, so \begin{align*} ...