# Examples of Hilbert spaces

Throughout my education I've encountered the following examples of Hilbert spaces: 1) the wave functions of a quantum mechanical system are elements of a Hilbert space 2) in the finite element method for solving PDEs solution can be approximated with functions which are elements of a Hilbert space.

Can you give me other examples where Hilbert spaces are encountered in Math/Science in general?

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Have you looked at the Wikipedia article (en.wikipedia.org/wiki/Hilbert_space)? It contains lots of examples. –  Fredrik Meyer Dec 8 '11 at 20:21

The space of weight $k$ cusp forms is a Hilbert space; the inner product is the Petersson inner product.