integral transform,mathematical operator that produces a new
function f1.5PT(y) by integrating the product of an existing
function F(x) and a so-called kernel function K(x, y) between
suitable limits. The process, which is called transformation, is
symbolized by the equation f1.5PT(y) =  ∫K(x, y)F(x)dxdx.
Several transforms are commonly named for the mathematicians who
introduced them: in the Laplace transform, the kernel is
exp(-xy) exy and the limits of integration are zero and plus
infinity; in the Fourier transform, the kernel is
(2π)-121PTexp(-ixy) 2π)−1/2eixy and the limits are minus and
plus infinity. (See also Fourier transform; Laplace transform.)
The value of integral transforms lies in Integral transforms are
valuable for the simplification that they bring about, most
often in dealing with differential equations subject to
particular boundary conditions. Proper choice of the class of
transformation usually makes it possible to convert not only the
derivatives in an intractable differential equatio