Spectral Decomposition of Analytic Functions under a q-Difference Operator

Puntos clave

• This research seeks to explore the spectral theory associated with a linear q-difference operator on analytic functions.
• Developed an invariant spectral decomposition for the q-difference operator.
• Characterized the kernel through mathematical analysis of operator dynamics.
• Derived iterated spectral dynamics to illustrate underlying principles.
• Establishes a novel invariant spectral decomposition for the linear q-difference operator.
• Reveals the emergence of an alternating binomial hierarchy related to spectral structure.