On Inverses of Discrete Rough Hilbert Transforms

TL;DR

This paper investigates the structure of the resolvent of the discrete rough truncated Hilbert transform at the critical exponent, extending previous results to better understand its inverse properties.

Contribution

It provides a detailed description of the resolvent structure of the discrete rough truncated Hilbert transform at the critical exponent, advancing theoretical understanding.

Findings

Resolved the structure of the resolvent at the critical exponent

Extended previous results on discrete rough Hilbert transforms

Enhanced understanding of inverse properties of the transform

Abstract

We describe the structure of the resolvent of the discrete rough truncated Hilbert transform under the critical exponent. This extends the results obtained in [8].