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Abstract
We construct a globally invertible analytic model for functions in the Hardy space H2(C+) [6, 17] via an explicit atomic system {Φn}, where each atom is defined to satisfy analyticity, completeness, stability, and modulator regularity [7, 4] by construction. No external hypotheses are required; all structural properties are encoded directly. The family {Φn} forms a Riesz basis of H2(C+) [3], yielding a unique and stable expansion f (s) = ∞ cnΦn(s), f ∈ H2(C+), n=1 which is globally invertible: coefficients can be recovered from analytic data, and synthesis reconstructs the function uniformly on compact subsets [14]. This construction provides a fully explicit, logically self-contained framework for ana- lyzing analytic functions with growth and symmetry constraints, and suggests applications to L-functions and other areas of analytic number theory [15, 1, 5].
