nLab
Laplace transform

Contents

Idea

The Laplace transform of a function ff on a suitable affine space is the result of an integration of the form

f^(a)f(x)e xadx, \hat f(a) \coloneqq \int f(x) e^{- x a} \, d x \,,

when defined.

For imaginary numbers aa, this is the Fourier transform. If aa is allowed to be a complex number, this is also called the Fourier-Laplace transform.

References

Created on October 31, 2017 at 05:15:55. See the history of this page for a list of all contributions to it.