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A strongly tempered Meyer space of countably infinite Hamel dimension

Jamie Martin

Palomar Registrypalomar/PALOMAR-2026-10-08-000002Oct 8, 2026math.CAscore 0

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…

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