In mathematics and control theory, H2, or H-square is a Hardy space with square norm.
In particular, it is a reproducing kernel Hilbert space.
is the set of square-integrable functions on the positive real number line, and
It is more; it is an isomorphism, in that it is invertible, and it isometric, in that it satisfies The Laplace transform is "half" of a Fourier transform; from the decomposition one then obtains an orthogonal decomposition of
into two Hardy spaces This is essentially the Paley-Wiener theorem.