The Efficient Computation of Fourier Transforms on Semisimple Algebras

We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier transform for a large class of finite groups. We continue to...

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Bibliographic Details
Published in:	The Journal of fourier analysis and applications Vol. 24; no. 5; pp. 1377 - 1400
Main Authors:	Maslen, David, Rockmore, Daniel N., Wolff, Sarah
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-10-2018 Springer Springer Nature B.V
Subjects:	Abstract Harmonic Analysis Algebra Algorithms Approximations and Expansions Computer science Fourier Analysis Fourier transforms Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing 05E40 Quiver Path algebra Fast Fourier transform 43A30 Bratteli diagram 20C15 65250
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Summary:	We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier transform for a large class of finite groups. We continue to find efficiencies by exploiting a connection between Bratteli diagrams and the derived path algebra and construction of Gel’fand–Tsetlin bases. Particular results include highly efficient algorithms for the Brauer, Temperley–Lieb, and Birman–Murakami–Wenzl algebras.
ISSN:	1069-5869 1531-5851
DOI:	10.1007/s00041-017-9555-5