On operator fields in the upper triangular Toeplitz form
Functional Analysis
2025-10-16 v1 Analysis of PDEs
Differential Geometry
Abstract
In this work, we solve the fundamental problem of describing the coordinate transformations that preserve the upper triangular Toeplitz form of the given operator field. Surprisingly, this problem is closely related to the description of all Nijenhuis operators in the same form. This description, as well as the formulas for the aforementioned coordinate transformations, are given by the implicit formulas involving matrix-valued functions.
Keywords
Cite
@article{arxiv.2510.12923,
title = {On operator fields in the upper triangular Toeplitz form},
author = {M. M. Chernin and A. Yu. Konyaev},
journal= {arXiv preprint arXiv:2510.12923},
year = {2025}
}