Integral Transform

A general integral transform is defined by

$$g(\alpha) = \int^b_a f(t)K(\alpha,t)\,dt,$$

where $K(\alpha,t)$ is called the Kernel of the transform.

See also Fourier Transform, Fourier-Stieltjes Transform, H-Transform, Hadamard Transform, Hankel Transform, Hartley Transform, Hough Transform, Operational Mathematics, Radon Transform, Wavelet Transform, Z-Transform

References

Integral Transforms

Arfken, G. ``Integral Transforms.'' Ch. 16 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 794-864, 1985.

Carslaw, H. S. and Jaeger, J. C. Operational Methods in Applied Mathematics. New York: Dover, 1963.

Davies, B. Integral Transforms and Their Applications, 2nd ed. New York: Springer-Verlag, 1985.

Poularikas, A. D. (Ed.). The Transforms and Applications Handbook. Boca Raton, FL: CRC Press, 1995.

Zayed, A. I. Handbook of Function and Generalized Function Transformations. Boca Raton, FL: CRC Press, 1996.