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Research questionHow can continuous multivariate unitary maps be decomposed into univariate components near identity, and what blocks global extension?A multivariate map into a noncommutative unitary group must coordinate variable dependence with matrix multiplication. Local behavior near the identity may fail to extend globally because of the group’s topology.
Research Paper
Latest papersRecent research connected to this question, newest first.Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued mapsThe source concerns continuous maps of several variables into \(\mathcal{U}(n)\), within an open 1-neighborhood of the identity. It establishes additive and sequential-factorized local representations and gives an \(\mathcal{SU}(2)\) lifting counterexample to global extension; it does not establish a global representation.research paper · Sep 4, 2026
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