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Exact db2 cascade norms and an optimal uniform constant

Jaime Enrique Lincovil Curivil, César Daniel Reinoso Reinoso, Niels Pacheco-Barrios

Palomar Registrypalomar/PALOMAR-2026-10-19-000005Oct 19, 2026math.FAscore 0

Exact supremum-operator norms for the undecimated periodic db2 cascade. For every level j and every period N at least the support, the norm is c_j^d, where c_j = 1651/1395 - (4/63)4^{-j} + (1/180)16^{-j} - (1/1736)32^{-j}. For every positive period, aliasing included, the norm is at most (1651/1395)^d, and that power is the least constant with this uniform role. The free mass is strictly increasing, converges to 1651/1395, and the gap is at most (4/63)4^{-j}. Dimension zero is exactly 1. N at least the support is sufficient, not claimed necessary, and one fixed period is not claimed to…

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