Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
Have you looked at the Wikipedia article ( It contains lots of examples. – Fredrik Meyer Dec 8 '11 at 20:21

Reproducing Kernel Hilbert spaces are fundamental to many machine learning algorithms.

share|cite|improve this answer

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

Added: In view of your first example, I decided to add this comment. According to the introduction of the book Modular forms and string duality, it seems that modular forms (of which cusp forms are an important example) are related to different dualities and symmetries appearing in string theory, mainly via the arithmetic of Calabi-Yau manifolds/varieties.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.