{"id":"palomar/PALOMAR-2026-10-19-000005","url":"https://github.com/jelincovil/tws-palomar/tree/eb2e7a7e48a5c96450bd514fb9346f3be1119e70","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000005-v1.json","repo":"https://github.com/jelincovil/tws-palomar","tags":["math.FA","math.NA","msc:42C40","msc:47A30","msc:68V20","wavelets","numerical-analysis","operator-norms"],"score":0,"title":"Exact db2 cascade norms and an optimal uniform constant","trust":"high","domain":"math.FA","source":"palomar","authors":["Jaime Enrique Lincovil Curivil","César Daniel Reinoso Reinoso","Niels Pacheco-Barrios"],"reviews":0,"subject":"math.FA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true,"formalizes":[{"title":"Explicit L-infinity stability bounds for undecimated Daubechies smoothing and wavelet-filtered persistence landscapes","identifier":"","relationship":"formalizes"},{"title":"TWS predecessor formalization in tws-repro","identifier":"https://github.com/jelincovil/tws-repro/tree/6f11e6e37039c40fd924146e2d5efdd531950179","relationship":"adapts"},{"title":"Previous tws-palomar Comparator wrapper","identifier":"https://github.com/jelincovil/tws-palomar/tree/f15103f97a300cfa243991956fa2d89e9c9ab6a7","relationship":"adapts"}]}