On some topics of analysis on noncommutative spaces
Operator Algebras
2016-12-15 v1 Analysis of PDEs
Abstract
We consider a conservative Markov semigroup on a semi-finite -algebra. It is known that under some reasonable assumptions it is enough to determine a kind of differential structure on such a 'noncommutative space'. We construct an analogue of a Riemannian metric in this setting, formulate a Poincar\'e-type inequality, provide existence and uniqueness results for quasi-linear elliptic and parabolic PDEs defined in terms of the constructed noncommutative calculus.
Keywords
Cite
@article{arxiv.1612.04371,
title = {On some topics of analysis on noncommutative spaces},
author = {Danila Zaev},
journal= {arXiv preprint arXiv:1612.04371},
year = {2016}
}