Connection of hypocoercivity and hypocontractivity via the Cayley transform
Dynamical Systems
2026-01-15 v1
Abstract
The concepts of hypocoercivity and hypocontractivity and their relationship are studied for semi-dissipative continuous-time and discrete-time evolution equations in a Hilbert space setting. New proofs for the characterization of the short-time decay of the solution from the initial value are presented, that in particular characterize the constants in the leading terms of the solution when expanded in time. Maximally coercive/contractive representations of hypocoercive and hypocontractive semi-dissipative systems are presented, as well as the effect of different representations on the error estimates for the numerical solution.
Cite
@article{arxiv.2601.09656,
title = {Connection of hypocoercivity and hypocontractivity via the Cayley transform},
author = {Anton Arnold and Stefan Egger and Volker Mehrmann and Eduard A. Nigsch},
journal= {arXiv preprint arXiv:2601.09656},
year = {2026}
}
Comments
39 pages, 2 figures