# Mellin transforms

January 29, 2021 — August 28, 2022

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“An integral transform with scale invariance like the Fourier transform has shift invariance.” From my perspective, it’s useful for analysing multiplicative products of random variables, their reciprocals and powers, much as the Fourier transform is useful for sums of scaled random variables.

For now, see the Mellin transform on Wikipedia.

Approachable references seem to be Bertrand, Bertrand, and Ovarlez (2000);Flajolet, Gourdon, and Dumas (1995);Galambos and Simonelli (2004).

## 1 Incoming

## 2 References

*Function Spaces and Potential Theory*.

*The Transforms and Applications Handbook*. The Electrical Engineering Handbook Series.

*Handbook of Mellin Tranforms*. Advances in Applied Mathematics.

*IEEE Transactions on Signal Processing*.

*Integral Transforms and Their Applications*.

*EURASIP J. Appl. Signal Process.*

*Integral Transforms and Their Applications*.

*Advances in Applied Mathematics*.

*Theoretical Computer Science*.

*Products of random variables : applications to problems of physics and to arithmetical functions*.

*The Annals of Applied Probability*.

*Proceedings of the Physical Society. Section A*.

*arXiv:1905.10733 [Cs, Math, Stat]*.

*DAFX (Digital Audio Effects)*.

*Journal of Applied Probability*.

*Handbook of Integral Equations*.

*The Transforms and Applications Handbook*. The Electrical Engineering Handbook Series.

*The Laplace Transform: Theory and Applications*.

*Real Analysis*. A Comprehensive Course in Analysis 1.0.

*Handbook of Function and Generalized Function Transformations*.