7. Extensions of the Fourier transform concept
The Fourier transform has proved so useful, in so many applications, that many mathematicians have generalized it, or described other transformations with similar properties. In this section, we describe some of them.
7.1 Laplace transformation
This transformation actually predates Fourier's in historical terms. It was used by Laplace for real functions in 1812; its inverse was explained by Poisson in 1820. It was subsequently generalized and, today, the Fourier transform can be considered a special case. However, the Laplace transform of distributions cannot be defined so simply. The following is a brief overview of its various characteristics, without proof or details.
The Ultimate Scientific and Technical Reference
This article is included in
Mathematics
This offer includes:
Knowledge Base
Updated and enriched with articles validated by our scientific committees
Services
A set of exclusive tools to complement the resources
Practical Path
Operational and didactic, to guarantee the acquisition of transversal skills
Doc & Quiz
Interactive articles with quizzes, for constructive reading
Extensions of the Fourier transform concept
References
The Ultimate Scientific and Technical Reference
