Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
79/2005
Differentiable $L^p$-functional calculus for certain sums of non-commuting operators
Michael Gnewuch
Abstract
We consider a special class of sums of non-commuting positive operators on $L^2$-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable $L^p$-functional calculus for $1\leq p \leq \infty$. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.