What question did this study set out to answer?

This research seeks to explore the spectral theory associated with a linear q-difference operator on analytic functions.

June 27, 2026Open Access

Spectral Decomposition of Analytic Functions under a q-Difference Operator

Key Points

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.

Abstract

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.

Spectral Decomposition of Analytic Functions under a q-Difference Operator

Key Points

Abstract

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