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44: Integral transforms, operational calculus


Introduction

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.

History

Applications and related fields

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 [Schematic of subareas and related areas]

Subfields

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

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

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


Textbooks, reference works, and tutorials

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

Software and tables

Integral transforms software. Laplace transform package for Mathematica

Other web sites with this focus

Selected topics at this site


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Last modified 2000/01/14 by Dave Rusin. Mail: