Orthonormal basis functions for L^2(R)

[mnb96]

Hello,

are there sets of functions that form an orthonormal basis for the space of square integrable functions over the reals L²(ℝ)?
According to Wikipedia the hermite polynomials form an orthogonal basis (w.r.t. to a certain weight function) for L²(ℝ). So I guess it would be a matter of multiplying the polynomials by suitable scalars in order to make them orthonormal.
Are there other known examples besides the Hermite polynomials?

 

[micromass]

You should do some research on wavelets. For example, the Haar wavelet gives an orthonormal basis apparently: http://en.wikipedia.org/wiki/Haar_wavelet

 

[mnb96]

Hi micromass!
thanks for your reply. Your answer basically answer my question.
Apparently the Haar wavelets "constitute a complete orthogonal system for the functions on the unit interval".

I was now wondering if there are more orthonormal bases for functions in L²(ℝ) whose support is the whole real line, e.g. rapidly decaying functions.