The Fourier Transform
The concept of an integral transform is undoubtedly familiar to the reader in its manifestation as the Laplace transform. This is a useful mechanism for handling certain differential equations. In general, integral transforms are helpful in problems where there is a function f to be determined from an equation that it satisfies. A judiciously chosen transform is then applied to that equation, the result being a simpler equation in the transformed function F. After this simpler equation has been solved for F, the inverse transform is applied to obtain f. We illustrate with the Laplace transform.
KeywordsFourier Transform Sobolev Space Compact Support Banach Algebra Inverse Fourier Transform
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