Partial Difference Equations Over Compact Abelian Groups
summary
Studies measurable circle-valued functions on compact abelian groups that satisfy K-fold partial difference equations and proves the quotient by “degenerate” (sum-of-simpler) solutions is a discrete list with separation bounded only by K. Gives an algorithmic (impractical) computation via measurable group cohomology and compactness, exhibits exact solutions (phase polynomials, sums of subgroup-invariant pieces and fractional-part/cohomology constructions), and a stability 99%→ε result: near-maximal U^K norm forces L1 proximity to an exact solution. No simple closed-form classification is found.
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