Operator Theory and Analytic Extensions of the Golden Equation Framework
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Description
This paper extends the Golden Equation alpha(k) + alpha(k)^(-k) = 2 framework introduced in the companion paper on k-bonacci constants to operator-theoretic and analytic contexts. It develops links between exponential growth constants, spectral theory, and functional analysis, showing that decay and recurrence phenomena share a common analytic structure across discrete and continuous systems.
Connections are established with linear and nonlinear differential equations, Fourier series decay, Hilbert space operators, and Hölder regularity. The spectral radius, moment growth, and analytic continuation are unified through a k-parameter mapping. The results demonstrate that the same analytic continuation governing k-bonacci sequences also describes the asymptotics of ODE, PDE, and harmonic systems, forming a continuous analytic bridge between recurrence theory and operator theory.
(Sequel to ‘Analytic Continuation of k-bonacci Constants’)
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GOLDEN_EQUATION__PAPER_2__The_Golden_EXTENSIONS (2).pdf
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Additional titles
- Subtitle (English)
- (Sequel to 'Analytic Continuation of k-bonacci Constants')
Related works
- Is supplement to
- Preprint: 10.5281/zenodo.17509903 (DOI)
- Is supplemented by
- Preprint: 10.5281/zenodo.17528956 (DOI)
References
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