Editing Generalized Fourier series (section)

{{Short description|Decompositions of inner product spaces into orthonormal bases}}
{{Use American English|date = March 2019}}
{{tone|date=February 2024}}
A '''generalized Fourier series''' is the expansion of a [[square integrable]] function into a sum of square integrable [[orthogonal basis | orthogonal basis functions]]. The standard [[Fourier series]] uses an [[orthonormal basis]] of [[trigonometric functions]], and the series expansion is applied to periodic functions. In contrast, a generalized Fourier series uses any set of orthogonal basis functions and can apply to any [[Square-integrable function|square integrable function]].<ref>Herman p.82</ref><ref>Folland p.84</ref>