Moutard transform approach to generalized analytic functions with contour poles

TL;DR

This paper extends Moutard transform techniques to generalized analytic functions with contour poles, demonstrating local transformation to regular functions and invertibility of the transforms, advancing the mathematical understanding of these functions.

Contribution

It introduces a method to transform generalized analytic functions with contour poles into regular functions using Moutard transforms, showing local invertibility.

Findings

Contour poles can be removed via Moutard transforms

Transforms are locally invertible

Generalized analytic functions can be regularized locally

Abstract

We continue studies of Moutard-type transforms for the generalized analytic functions started in arXiv:1510.08764, arXiv:1512.00343. In particular, we show that generalized analytic functions with the simplest contour poles can be Moutard transformed to the regular ones, at least, locally. In addition, the later Moutard-type transforms are locally invertible.