Constructs the dimension-shift category Dim+ and classifies scaling-covariant functors to Radon measures, with Gaussian normalization yielding the Mellin-Gamma measure whose transports recover ball volumes V(x) and radial integrals R(x,r), related by a coboundary identified with categorical O_t-dim.
Boas, Entire Functions, Academic Press, 1954
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The Dimension-Shift Category and Its Mellin-Gamma Representation
Constructs the dimension-shift category Dim+ and classifies scaling-covariant functors to Radon measures, with Gaussian normalization yielding the Mellin-Gamma measure whose transports recover ball volumes V(x) and radial integrals R(x,r), related by a coboundary identified with categorical O_t-dim.