Abstract
Given a finite group \(G\) and a subgroup \(H\le G\), we develop a Fourier analysis for \(H\)-conjugacy invariant functions on \(G\), without the assumption that \(H\) is a multiplicity-free subgroup of \(G\). We also study the Fourier transform for functions in the center of the algebra of \(H\)-conjugacy invariant functions on \(G\). We show that a recent calculation of Cesi is indeed a Fourier transform of a function in the center of the algebra of functions on the symmetric group that are conjugacy invariant with respect to a Young subgroup.
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Communicated by K. Gröchenig.
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Scarabotti, F., Tolli, F. Fourier analysis of subgroup conjugacy invariant functions on finite groups. Monatsh Math 170, 465–479 (2013). https://doi.org/10.1007/s00605-012-0445-2
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DOI: https://doi.org/10.1007/s00605-012-0445-2