Integral transforms

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Useful for solving various integral equations and PDEs. Fourier transforms, Laplace transforms, Mellin transforms, Hankel transforms…

Free resource: The transforms and applications handbook / edited by Alexander D. Poularikas. (Poularikas 2000)

Fourier transform

See Fourier transforms.

Laplace transform


Hankel transform

TBD. Covered implicitly in rotational symmetries.

Mellin transform

A transform with “Scale invariance like the Fourier transform has shift invariance”. Sounds fun.


Adams, David R., and Lars I. Hedberg. 1999. Function Spaces and Potential Theory. Springer Science & Business Media.
Bruda, Glenn. 2022. Maclaurin Integration: A Weapon Against Infamous Integrals.” arXiv.
Brychkov, I︠U︡ A., O. I. Marichev, and Nikolay V. Savischenko. 2019. Handbook of Mellin Tranforms. Advances in Applied Mathematics. Boca Raton: CRC Press, Taylor & Francis Group.
Davies, Brian. 2002. Integral Transforms and Their Applications. 3rd edition. New York: Springer.
Debnath, Lokenath, and Dambaru Bhatta. 2014. Integral Transforms and Their Applications. 3rd edition. Chapman and Hall/CRC.
Polyanin, A. D., and A. V. Manzhirov. 1998. Handbook of Integral Equations. Boca Raton, Fla: CRC Press.
Poularikas, Alexander D., ed. 2000. The Transforms and Applications Handbook. 2nd ed. The Electrical Engineering Handbook Series. Boca Raton, Fla: CRC Press.
Schiff, Joel L. 1999. The Laplace Transform: Theory and Applications. 1999th edition. New York: Springer.
Simon, Barry. 2015. Real Analysis. A Comprehensive Course in Analysis 1.0. UNIVERSITIES PRESS.

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