Time-Frequency Analysis and Representations of the Discrete Heisenberg Group
Chapter
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Abstract
The operators [ϱ ω (j, k, l)f](t) = e2πiωl e2πiωkt f(t + j) on \(L^{2}(\mathbb{R})\) constitute a representation of the discrete Heisenberg group. We investigate how this representation decomposes as a direct integral of irreducible representations. The answer is quite different depending on whether ω is rational or irrational, and in the latter case it provides illustrations of some interesting pathological phenomena.
Keywords
Discrete Heisenberg group Unitary representations Direct integral decompositionsReferences
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