Generalized analytic functions, Moutard-type transforms and holomorphic maps

TL;DR

This paper extends the theory of Moutard-type transforms for generalized analytic functions, interpreting them as spinor fields and demonstrating their compatibility with holomorphic variable changes.

Contribution

It introduces a spinor field interpretation of generalized analytic functions and proves that Moutard-type transforms commute with holomorphic transformations.

Findings

Moutard-type transforms can be viewed as spinor fields.

These transforms commute with holomorphic changes of variables.

The approach generalizes previous studies of analytic functions.

Abstract

We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with holomorphic changes of variables.