{"id":"palomar/PALOMAR-2026-10-08-000002","url":"https://github.com/balancedscorpion/countably-infinite-dimension-strong-meyer-spaces/tree/4d3163a0ce1dd93fa48b7d4677fe78db15c0af9c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-08-000002-v1.json","repo":"https://github.com/balancedscorpion/countably-infinite-dimension-strong-meyer-spaces","tags":["math.CA","math.FA","msc:42A38","msc:46F12","msc:52C23","fourier-analysis","meyer-sets","tempered-distributions"],"score":0,"title":"A strongly tempered Meyer space of countably infinite Hamel dimension","trust":"high","domain":"math.CA","source":"palomar","authors":["Jamie Martin"],"reviews":0,"subject":"math.CA","summary":"There exists a locally finite carrier Λ in the real line whose whole complex strongly tempered Meyer space has Hamel dimension ℵ₀. Both a tempered distribution and its distributional Fourier transform have local atomic formulas on Λ, with coefficient families whose absolute values are summable after division by some polynomial weight (1 + |x|)^N. The same carrier supports the entire space; finite-dimensional exponent layers prove the rank upper bound and independent original parity modes prove the lower bound. The radius schedule is selected classically. This is an existence theorem for one…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-08","reactions":{},"formalized":true,"formalizes":[{"title":"Whole strongly tempered Meyer space of Hamel dimension aleph0 (PR #653)","identifier":"https://github.com/ls558/MeyerGeneralProblem/pull/653","relationship":"formalizes"}]}