Fourier transform

ID: fourier-transform

Fourier transform by Ciro Santilli 37 Updated +Created
Continuous version of the Fourier series.
Of course, every function defined on a finite line segment (i.e. a compact space).
Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.

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