# Divergence of wavelet series: A multifractal analysis

## TL;DR

This paper investigates the divergence behavior of wavelet series using multifractal analysis, establishing bounds on divergence sets' Hausdorff dimensions and demonstrating their optimality under generic conditions.

## Contribution

It introduces a multifractal framework to analyze pointwise divergence of wavelet series and provides deterministic bounds that are shown to be generically optimal.

## Key findings

- Deterministic upper bounds for Hausdorff dimensions of divergence sets
- Bounds depend on the sequence space of wavelet coefficients
- Bounds are generically optimal under various notions of genericity

## Abstract

We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence occurs, and we show that these bounds are generically optimal, according to several notions of genericity.