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. We study the third moment for functions on arbitrary compact Lie groups. We use techniques of representation theory to generalize the notion of band-limited functions in classical Fourier theory to functions on the compact groups \ (SU (n), SO (n), Sp (n) \). We then prove that for generic band-limited functions the third moment or its Fourier equivalent, the bispectrum, determines the function up to translation by a single unitary matrix. Moreover, if \ (G=SU (n) \) or \ (G=SO (2n+1) \), we prove that the third moment determines the \ (G\) -orbit of a band-limited function. As a corollary, we obtain a large class of finite-dimensional representations of these groups for which the third moment determines the orbit of a generic vector. When \ (G=SO (3) \) this gives a result relevant to cryo-EM, which was our original motivation for studying this problem. Keywordsorbit recoverybispectrumMSC codes94A1222D10
Edidin et al. (Tue,) studied this question.