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Research questionHow should frequency-based smoothness be defined on non-abelian groups without a canonical ordering of irreducible representations?For functions on the real line, smoothness is associated with Fourier concentration at low frequencies. Non-abelian groups lack a canonical ordering of irreducible representations, so the meaning of low frequency—and therefore smoothness—depends on additional group structure.
Research Paper
Latest papersRecent research connected to this question, newest first.What is Smoothness?The source studies orderings induced by symmetric generating sets and Cayley-graph Laplacians, characterizes the freedom allowed by natural axioms, and examines extensions to compact groups and finite transitive group actions. It supports conclusions about the dependence of smoothness on the group and generating set.research paper · Sep 3, 2026
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