Mathematics > Functional Analysis
[Submitted on 21 Dec 2018]
Title:Spatio-spectral limiting on hypercubes: eigenspaces
View PDFAbstract:The operator that first truncates to a neighborhood of the origin in the spectral domain then truncates to a neighborhood of the origin in the spatial domain is investigated in the case of Boolean cubes. This operator is self adjoint on a space of bandlimited signals. The eigenspaces of this iterated projection operator are studied and are shown to depend fundamentally on the neighborhood structure of the cube when regarded as a metric graph with path distance equal to Hamming distance.
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