Bounding the Local Dimension of the Convolution of Measures

TL;DR

This paper investigates how the local dimension of the convolution of two measures can be bounded based on the local dimension of one measure, providing formulas for special points in the support.

Contribution

It introduces conditions for bounding the local dimension of convolutions and derives formulas for specific points, advancing understanding of measure convolutions.

Findings

Bounded the local dimension of convolutions under certain conditions.

Derived formulas for local dimensions at special points.

Provided insights into the structure of convoluted measures.

Abstract

We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension of some special points in the support of the convolution.