Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
Complex Variables
2024-09-06 v6 Analysis of PDEs
Rings and Algebras
Abstract
We recall known and establish new properties of the Dieudonn\'e and Moore determinants of quaternionic matrices.Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. Then we introduce and briefly discuss quaternionic Monge-Amp\'ere equations.
Cite
@article{arxiv.math/0104209,
title = {Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:math/0104209},
year = {2024}
}
Comments
42 pages. A mistake in the statement of Theorem 1.2.4(iii) corrected