A general integral transform is defined by
where
is called the integral kernel of the 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-Transform
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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 Transform
Cite this as:
Weisstein, Eric W. "Integral Transform."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IntegralTransform.html
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