Mahler coefficients of uniformly differentiable locally scaling functions on ℤ2

Key Points

• This research aims to connect uniformly differentiable locally scaling functions with ergodic transformations and to derive conditions for their differentiability.
• Utilized finite-difference operator to establish a relationship between functions and transformations
• Analyzed Mahler coefficients in relation to the differentiability of locally scaling functions
• Identified necessary and sufficient conditions for uniform differentiability
• Established a clear link between the properties of scaling functions and ergodic transformations