Efficient computation of Fourier transforms on compact groups
type: Item
instance of: scholarly article
title: Efficient computation of Fourier transforms on compact groups
zbMATH Open document ID: 0914.43004
DOI: 10.1007/BF02475926
author: David K. Maslen
published in: The Journal of Fourier Analysis and Applications
publication date: 1999-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/59551
review text: The paper describes a fast Fourier transform algorithm for the computation of Fourier transforms on compact Lie groups. For a given compact Lie group \(G\), a finite subset \(X\) of \(G\), a finite set \(R\) of finite dimensional representations of \(G\), and a complex valued function \(f\) on \(X\), the aim is to efficiently compute \[ F(\rho)=\sum_xx\in Xf(x)\rho(x) \] for all \(\rho\in R\). For each positive integer \(b\), let \(R=R_b\) denote the set of irreducible unitary representations of \(G\) that have highest weight with norm at most \(b\). Subsets \(X=X_b\) are defined of the classical groups for which the above calculation may be performed relative to Gel'fand-Tsetlin bases in \(O(b^{\dim G+\gamma(G)})\) operations, where \(\gamma(G)\) depends on the classical group in question. Finally, analogous computations are considered on homogeneous spaces, and for finite sets \(R=D\) of distributions.
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 43-04
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1220785
zbMATH Keywords: Fourier transform
zbMATH Keywords: compact Lie groups
zbMATH Keywords: irreducible unitary representations
zbMATH Keywords: classical groups
zbMATH Keywords: Gel'fand-Tsetlin bases
zbMATH Keywords: homogeneous spaces
reviewed by: Karl-Heinz Zimmermann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1220785