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[Texts]## 44: Integral transforms, operational calculus |

Integral transforms include the Fourier transform (see section 43) as well as the transforms of Laplace, Radon, and others. (The general theory of transformations between function spaces is part of Functional Analysis, section 46) Also includes convolution operators and operational calculi.

For fractional derivatives and integrals, See 26A33. For Fourier transforms, See 42A38, 42B10. For integral transforms in distribution spaces, See 46F12. For numerical methods, See 65R10

There is only one division (44A) but it is subdivided:

- 44A05: General transforms, See also 42A38
- 44A10: Laplace transform
- 44A12: Radon transform, See also 92C55
- 44A15: Special transforms (Legendre, Hilbert, etc.)
- 44A20: Transforms of special functions
- 44A30: Multiple transforms
- 44A35: Convolution
- 44A40: Calculus of Mikusinski and other operational calculi
- 44A45: Classical operational calculus
- 44A55: Discrete operational calculus
- 44A60: Moment problems
- 44A99: Miscellaneous topics

This is one of the smallest areas in the Math Reviews database.

Browse all (old) classifications for this area at the AMS.

Widder, D. V.: "What is the Laplace transform?" Amer. Math. Monthly 52, (1945). 419--425. MR7,155c

- Here are the AMS and Goettingen resource pages for area 44.

- What's an intuitive description of the Laplace transform?
- Relationship between Laplace and Fourier transforms?
- Finding the inverse Laplace transform
- Applications of kernel functions to the solutions of PDEs.
- What is Van der Corput's Lemma (on boundedness of integral transforms)

Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org