Factorization method on time scales
Tomasz Goli\'nski

TL;DR
This paper introduces a factorization method for second order difference equations on time scales, constructing Hilbert spaces and ladder operators to generate solutions, bridging continuous and discrete analysis.
Contribution
It develops a novel factorization approach for second order difference equations on time scales, including the construction of Hilbert spaces and ladder operators.
Findings
Constructed Hilbert spaces on time scales
Developed ladder operators for difference equations
Generated new solutions via eigenproblem factorization
Abstract
We present an approach to the factorization method for second order difference equations on time scales. We construct Hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order -difference operators in the sense that and act as ladder operators generating new solutions of eigenproblem of .
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