On the scaling limit of a singular integral operator

TL;DR

This paper investigates the behavior of a specific singular integral operator, deriving its scaling limit and Schauder bounds, which are crucial for understanding its analytical properties in the context of monodromy problems.

Contribution

It introduces a new analysis of a singular integral operator related to monodromy, providing scaling limits and Schauder bounds that were not previously established.

Findings

Derived the scaling limit of the operator

Established Schauder bounds for the operator

Enhanced understanding of monodromy-related integral operators

Abstract

The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems.