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March 10, 2026Open Access

Fourier Decay Under a Radial Ibaguner Fractal Operator A Rigorous Component of the Falconer-IFO Program

Key Points

This research aims to explore the Fourier decay properties of measures under a radial Ibaguner Fractal Operator.
Analyzed Fourier decay of measures using a radial Ibaguner Fractal Operator.
Established decay rates for Frostman measures of dimension s.
Examined sharp dimensional thresholds for positivity of IFO-distance sets.
Demonstrated a specific decay rate for pushforward measures under Hlder-type contraction.
Identified a clear dimensional threshold for the associated IFO-distance set.

Abstract

We analyze Fourier decay properties of measures under a radial Ibaguner Fractal Operator (IFO). For Frostman measures of dimension s, we establish a decay rate for the pushforward measure under a Hlder-type radial contraction. This yields a sharp dimensional threshold for positivity of the associated IFO-distance set.

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