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integral transform (Definition)

A generic integral transform takes the form

$\displaystyle F(p) = \int_\alpha^\beta K(p, t) f(t)dt,$
with $ p$ being the transform parameter.

Note that the transform takes a function $ f(t)$ and produces a new function $ F(p)$.

The function $ K(p, t)$ is called the kernel of the transform. The kernel of an integral transform, along with the limits $ \alpha$ and $ \beta$, distinguish a particular integral transform from another.

Examples



"integral transform" is owned by PrimeFan. [ full author list (4) | owner history (5) ]
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See Also: contour integral, group homomorphism

Also defines:  kernel
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Cross-references: Fourier transform, Laplace transform, function, parameter
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This is version 6 of integral transform, born on 2002-04-05, modified 2008-06-19.
Object id is 2815, canonical name is IntegralTransform.
Accessed 7076 times total.

Classification:
AMS MSC65R10 (Numerical analysis :: Integral equations, integral transforms :: Integral transforms)

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