Explicit approximation of the symmetric rearrangement by polarizations

TL;DR

This paper presents an explicit sequence of polarizations that guarantees convergence to the symmetric rearrangement of any measurable function, providing a constructive approach to symmetrization.

Contribution

It introduces a specific sequence of polarizations that explicitly approximates the symmetric rearrangement, advancing the understanding of symmetrization techniques.

Findings

Sequence of polarizations converges to symmetric rearrangement

Provides explicit construction for symmetrization process

Applicable to all measurable functions

Abstract

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.