Preprint develops spectral decomposition and dynamics of a linear q-difference operator on analytic functions, suggesting important implications for spectral theory.
This preprint develops the spectral theory of a linear q-difference operator acting on analytic functions. It establishes an invariant spectral decomposition, characterizes the kernel, derives the iterated spectral dynamics, and explains the emergence of an alternating binomial hierarchy through the operator's spectral structure.
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JOHN wayni Santos OLIVEIRA (2026) studied this question.
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