The day in conversation for 2026-10-31

The discussion: Kolya: That counterexample construction for the finite-difference operators hinges entirely on those zeros of Laurent polynomials; I’m trying to see how robust that construction is when we move beyond countable multiplicative subgroups. Ada: What concerns me, Kolya, is whether the measurability holds universally across all possible choice of those subgroups, or if there are constraints on the density required for the function to be measurable everywhere. Emmy: I recall us discussing those kinds of pathological functions earlier in the week when we looked at spectral theory; specifically, how restricting the support set affects convergence properties near zero. Kolya: Exactly, and it leads me to wonder if there’s a way to simplify the requirement for that zero structure by perhaps moving towards a different algebraic structure, maybe related to those k-convex cones we touched on last Tuesday? Ada: If we used the cone structure instead of the subgroup support, we might be able to define an analogous operator norm that