Integral transform Guide, Meaning , Facts, Information and Description

In mathematics, an integral transform is any transform T of the following form:

Tf is a function of a parameter, denoted u in the equation above. Thus, an integral transform maps one function into another which is a function of the parameter.

There are several useful integral transforms. Each transform corresponds to a different choice of the function g, which is called the kernel of the transform.

Table of Integral Transforms

Transform	Symbol	Kernel
Laplace transform
Fourier transform
Hilbert transform
Mellin transform
Identity transform

Although the properties of integral transforms vary widely, they have some properties in common. For example, every integral transform is a linear operator, since the integral is a linear operator, and in fact if the kernel is allowed to be a generalized function then all linear operators are integral transforms (a properly formulated version of this statement is the Schwartz kernel theorem).

See also

• List of transforms
• List of Fourier-related transforms

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