A general integral transform is defined by
 |
where 
is called the integral kernel of the transform.
Integral Transform
See also
Buschman Transform, Fourier Transform, Fourier-Stieltjes Transform, G-Transform, H-Transform, Hadamard Transform, Hankel Transform, Hartley Transform, Hough Transform, Kontorovich-Lebedev Transform, Laplace Transform, Mehler-Fock Transform, Meijer Transform, Mellin Transform, Narain G-Transform, Operational Mathematics, Radon Transform, Stieltjes Transform, W-Transform, Wavelet Transform, Z-TransformExplore with Wolfram|Alpha
References
Arfken, G. "Integral Transforms." Ch. 16 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 794-864, 1985.Brychkov, Yu. A. and Prudnikov, A. P. Integral Transforms of Generalized Functions. New York: Gordon and Breach, 1989.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.Erdélyi, A.; Oberhettinger, M. F.; and Tricomi, F. G. Tables of Integral Transforms. Based, in Part, on Notes Left by Harry Bateman and Compiled by the Staff of the Bateman Manuscript Project, 2 vols. New York: McGraw-Hill, 1954.Krantz, S. G. "Transform Theory." Ch. 15 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 195-217, 1999.Marichev, O. I. Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables. Chichester, England: Ellis Horwood, 1982.Poularikas, A. D. (Ed.). The Transforms and Applications Handbook. Boca Raton, FL: CRC Press, 1995.Weisstein, E. W. "Books about Integral Transforms." http://www.ericweisstein.com/encyclopedias/books/IntegralTransforms.html.Zayed, A. I. Handbook of Function and Generalized Function Transformations. Boca Raton, FL: CRC Press, 1996.Referenced on Wolfram|Alpha
Integral TransformCite this as:
Weisstein, Eric W. "Integral Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IntegralTransform.html