We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for 1 ≤ p ≤ ∞. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-10,
author = {Michael Gnewuch},
title = {Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {105-125},
zbl = {1103.47014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-10}
}
Michael Gnewuch. Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators. Colloquium Mathematicae, Tome 106 (2006) pp. 105-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-10/