Completeness of an orthonormal system of vectors of a Hilbert space can be equivalently restated as:
2.
In other words, the Hermite functions form a complete orthonormal system of eigenfunctions for the Fourier transform on.
3.
Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the above, this equality implies the resolution of the identity:
4.
If we normalize the polynomials of Legendre, the coefficients of Fourier of the reducer ? related to this orthonormal system are null for an even index and are given by
5.
A system of vectors satisfying the first two conditions basis is called an orthonormal system or an orthonormal set ( or an orthonormal sequence if " B " is countable ).
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