Hello,(adsbygoogle = window.adsbygoogle || []).push({});

are there sets of functions that form anorthonormal basisfor the space of square integrable functions over the reals L^{2}(ℝ)?

According to Wikipedia the hermite polynomials form an orthogonal basis (w.r.t. to a certain weight function) for L^{2}(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orthonormal basis functions for L^2(R)

Loading...

Similar Threads for Orthonormal basis functions |
---|

A Infinite matrices and the Trace function |

I How to find admissible functions for a domain? |

I Diagonalization and change of basis |

I Measures of Linear Independence? |

B Tensor Product, Basis Vectors and Tensor Components |

**Physics Forums | Science Articles, Homework Help, Discussion**