nLab Laplace transform

Idea

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

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

when defined.

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

Related concepts

• Mellin transform

References

• Wikipedia, Laplace transform