Integral transforms


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The way we usually analytically solve integral equations and PDEs is via integral transforms. Fourier transforms, Laplace transforms, Mellin transforms, Hankel transforms…

Fourier transform

See Fourier transforms.

Laplace transform

TBD.

Hankel transform

TBD.

Mellin transform

TBD.

References

Adams, David R., and Lars I. Hedberg. 1999. Function Spaces and Potential Theory. Springer Science & Business Media.
Brychkov, IU 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. http://dsp-book.narod.ru/TAH/fm.pdf.
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.